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ASTRONOMY 



ASTRONOMY 

A HANDY MANUAL FOR 
STUDENTS AND OTHERS 



BY 

F. W. DYSON, F.R.S. 

ASTRONOMER ROYAL FOR SCOTLAND; 
PROFESSOR OF ASTRONOMY IN THE UNIVERSITY OF EDINBURGH 




WITH 95 DIAGRAMS AND II.LUSI RATIOXS 



NEW YORK 
E. P. DUTTON & CO. 

i 91 8 



QBH- 

.11 



All rights reserved 

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PREFACE 

In this little book I have attempted to give an 
account of the methods employed by astronomers and 
the reasons for some of the propositions they advance. 
Astronomical investigations frequently seem compli- 
cated owing to the amount of subsidiary detail, but 
the principles underlying them are simple and usually 
admit of a clear statement which can be followed by 
a general reader. In the introduction to his lectures 
delivered at Ipswich in 1848 Sir George Airy draws 
attention to an attitude towards Astronomy which is 
still prevalent. Such questions as the determination 
of the distance of the Sun or Moon are considered as 
beyond ordinary comprehension ; the instruments with 
which astronomical measurements are made are sup- 
posed to be based on obscure and difficult principles ; 
therefore the best a layman can do is to accept state- 
ments on the personal credit of the astronomer making 
them. He points out that this is an exaggerated 
view. The principles involved in measuring the dis- 
tance of the Moon are no more abstruse than those 
employed to find the distance of a tree on the other 
side of a river. Astronomical instruments are as 
simple in principle and far less complicated in detail 
than a lathe or a steam-engine. It is quite true that 
in both instruments and methods many subsidiary 
details must be attended to when great accuracy is 
required in order that disturbing causes may be 
allowed for or eliminated. But an explanation of 
the essential principles may be given which can be 
readily understood with ordinary care and attention. 



vi PREFACE 

As far as possible an historical order has been 
followed. The reader's attention has been drawn to 
the desirability of making for himself certain observa- 
tions of the sky which do not require the use of a 
telescope. Every educated person ought to see with 
his own eyes how Sun, Moon, Stars and Planets move 
in the sky, and be able to infer from his own observa- 
tions the movement of the Earth about the Sun, the 
comparative nearness of the Moon, and other common- 
places of Astronomy. 

It is difficult to acknowledge fully my obligations 
to the authors of books and papers which I have con- 
sulted. Mention should be specially made of Mr. 
Arthur Berry's History of Astronomy, Prof. Young's 
General Astronomy, and the articles by Prof. New- 
comb on " Astronomy" and Prof. Hale on " Spec- 
troscopy " in the Encyclopcedia Britannica. 

I am indebted to the Astronomer Royal Sir 
William Christie, Prof. Barnard, Prof. Ritchey and 
other astronomers for permission to reproduce photo- 
graphs published by them, and to Mr. W. B. Blaikie 
for the map taken from his Monthly Star Maps 
published by the Scottish Provident Association. 

I wish to express my thanks to a number of friends 
for help in various directions. Mr. Heath, first as- 
sistant of the Royal Observatory, Edinburgh, copied 
a number of photographs and supplied me with the 
drawing on p. 172 ; Mr. Storey, assistant at the 
Observatory, and Mr. MacGregor assisted with the 
diagrams. I am much obliged to Mr. Storey and to 
Dr. J. Reynolds Green, who read the book in proof, 
for their valuable criticism and suggestions. 

F. W. Dyson. 

Royal Observatory ; Edinburgh, 
March 7, igio. 



CONTENTS 



Chap. 

I Ancient Astronomy 

II The Copernican System 

III The Law of Gravitation 

IV Astronomical Instruments . 
V The Sun's Distance 

VI The Sun 

VII The Solar System . 

VIII Distances and Movements of the Stars 

IX Stars and Nebulae . 

X Double Stars and Clusters . 

XI Variable Stars and New Stars 

XII The Sidereal Universe 





Page 


• 


I 


• 


3° 


• 


45 




. 63 




85 




100 




129 


e Stars 


164 


• 


i93 




208 




225 




239 



CHAPTER I 

ANCIENT ASTRONOMY 

Astronomy is the oldest of the sciences. The 
orientation of the pyramids or of Stonehenge, the 
mythology of the Greeks and the religious festivals of 
the Jews are familiar evidences of astronomical know- 
ledge in early civilizations. The constant repetition, 
day by day, month by month, or year by year, of 
similar phenomena both invited and aided study of 
the heavenly bodies. Before the dawn of history men 
wondered what caused the rising and setting of the 
Sun and Moon each day, why the Moon went through 
her phases each month, and why Orion reappeared 
each year in the sky as surely as the seasons returned. 
An out-of-door life was favourable to a knowledge of 
the heavens, and the tribes of Chaldea and Arabia 
two or three thousand years ago were, perhaps, better 
acquainted with the appearance of the sky than we 
are to-day. Modern conditions of life are not favour- 
able to the general cultivation of practical astronomy, 
Buildings circumscribe the view of the sky, clocks and 
watches save us the trouble of observing the Sun and 
stars for time, and artificial illumination makes us 
independent of moonlight. But the following phe- 



2 ASTRONOMY 

nomena of the skies ought not to be merely read of in 
books, but should be verified by actual observation. 

(i) The diurnal movement of the Sun; the different 
positions of the Sun in the sky in summer and winter. 

(2) The phases of the Moon ; the rapid movement of 
the Moon among the stars. 

(3) The diurnal movement of the stars ; the appear- 
ance of different constellations at different times of the 
year. 

Observation of the Sun. — In the latitude of London the 
Sun rises on midsummer day at about 3 h. 45 m. 
at a point on the horizon considerably north of east. 
At midday, when due south, it is high in the sky. 
If we take a stick and point it horizontally and turn 
it gradually towards the . vertical, we shall not be 
pointing to the Sun till the stick has been turned 
through rather more than two-thirds of the right- 
angle between the horizontal and vertical directions. 
It sets in the evening about 8h. 19 m. at a point on 
the horizon considerably north of west. From mid- 
summer to midwinter it rises later and sets earlier 
each day; the point of the horizon where it rises 
gradually shifts from north of east to due east, and 
then to south of east ; and the point where it sets shifts 
in the other direction from north of west to due west, 
and then to south of west. In midwinter the Sun 
rises at 8 h. 7 m. and sets at 3 h. 51 m., and at noon, 
instead of being high up in the sky, it is only 15 , 
or one-sixth of a right-angle, above the horizon. 



ANCIENT ASTRONOMY 



From midwinter to midsummer the days lengthen 
and the Sun at noon is higher each day. Midway 
between midsummer and midwinter, on March 22 and 
Sep. 22, the Sun rises due east and sets due west, 
and day and night are equal in length. This succes- 
sion of phenomena repeats itself year by year, and is 
more striking in the latitude of the British Isles than 
in the more southern countries from which our 
astronomical knowledge was derived. 

Diagram I illustrates the path of the Sun across the 
sky at different times of the year. The circle NES is 
the horizon, and NPZS 
the meridian or circle of 
the sky cut by a vertical 
plane in a direction due 
north and south. The 
diagram represents the 
eastern half of the sky — 
the part above NES 
being above the horizon 
and visible, and the part 
below r NES below the 
horizon and invisible, On midsummer day the Sun 
travels from A to C between midnight and midday, 
crossing the horizon at B (i.e. rising) at 3 h. 45 m. 
All points of the circle ABC are 66J° from P, i. e. 
if we divide the arc of the sphere from the pole P to 
the opposite one into 180 parts, all points of the 

circle ABC are 66J parts from P. But on Septem- 

b 2 




Diag. I. 



4 ASTRONOMY 

ber 22 the Sun is 90 from P. At midnight on 
that day it is at D, rises at E (due east) at 6h. om., 
and is at its highest point F (due south) at 12 h. om. 
When we come to December 22 the Sun is 113J from 
P. At midnight it is at G, does not reach H, i. e. 
does not rise till 8 h. 7 m., and is at K (due south) at 
12 o'clock. 

Solar Day. — It is not quite correct to say that the Sun 
is due south exactly at 12 o'clock, but this is suffi- 
ciently true for the explanation given in the last 
paragraph. The interval of time between the moment 
when the Sun is due south one day to the moment 
when it is due south the next is called the solar day, 
and is the natural unit of time. The length of the solar 
day is not quite constant, but varies to the extent of 
one minute at different times of the year. Its average 
length throughout the year is the mean solar day, and 
is exactly the 24 hours of our clocks and watches. 

Year. — The exact time the Sun takes to go through 
the cycle of changes described above is the year. The 
length of the year can therefore be found approxi- 
mately by counting the number of days from a par- 
ticular day in any year to the day in the following 
year when the Sun is the same height in the sky at 
noon. When the Sun's height at noon, or, in tech- 
nical language, its altitude, is measured accurately, it 
is found that after 365 days have elapsed from March 
22 the Sun is not quite so high, but after 366 days is 
higher. Thus the year does not consist of an exact 
number of days. 



ANCIENT ASTRONOMY 5 

The Greek astronomer, Hipparchus, made accurate 
observations which showed that the year w<as rather 
less than 365J days — a year of 365J days giving, 
according to his calculations, an error of only one 
day in 300 years. 

Calendar. — It is hardly necessary to refer to the 
difficulties different nations experienced with their 
chronology till a civil year was devised, whose aver- 
age length was equal to that of the actual solar or 
tropical year. Our calendar is derived from the one 
introduced by Julius Caesar with the advice and assist- 
ance of Sosigenes. Every fourth year on this system 
is a leap year, and consists of 366 days. The error, 
according to this reckoning, is more than was sup- 
posed by Hipparchus, and is very approximately 3 
days in 400 years. In course of time this small error 
accumulated, till in 1582, the equinoxes, midsummer 
day, etc., all fell on dates 10 days different from those 
on which they had fallen in a.d. 325, the year of the 
Council of Nice. In the reformation of the calendar, 
which was then introduced by Pope Gregory XIII, it 
was ordained that the centurial years should not be 
counted as leap years unless the number of centuries 
is divisible by 4 without remainder. Thus 1700, 1800, 
1900 are not leap years, but 2000 is a leap year. With 
this correction the average length of the civil year 
only differs from the solar year by one day in about 
3300 years. 

Observation of the Moon. — Each month the Moon 
changes from new to full and from full to new. 



ASTRONOMY 



These changes in the Moon's appearance are called 
its phases, and observation shows that as the phase of 
the Moon changes the angle between the directions of 
the Sun and Moon changes also. The new Moon is 
always seen in the west near the setting Sun ; when 
half illuminated its direction makes a right-angle with 
that of the Sun ; and when full, its direction is 
diametrically opposite to that of the Sun. The correct 
interpretation of the Moon's phases was given by 
Aristotle (384-322 B.C.), viz. that it is a spherical 
body, illuminated by the very distant Sun. One half 
of the sphere is bright and the other dark. The 
appearance of the Moon from the Earth depends on 
whether the Earth is in a position from which much 
or little of the illuminated part is visible. 



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Diag. II. 

In the right half of Diagram II the appearance of 
the Moon is shown : (1) a few days after it is new; 
(2) shortly after first quarter; (3) full; (4) shortly be- 



ANCIENT ASTRONOMY 



fore third quarter; (5) a few days before it is new. 
In the left half the illuminated and unilluminated 
parts of the Moon are shown at corresponding times. 

Another observation which the reader should make 
consists in noting the position of the Moon with refer- 
ence to the stars on two consecutive nights. In this way 
its rapid movement across the sky will be duly appre- 
ciated. The distance moved in 24 hours will be found 
to be very considerable, approximately 12 , or ^th 
part of the whole circumference of the sky. Diagram 
III illustrates this : if the Moon is at M 1 one night, it 
will be at M 2 at the same time on the following night. 

Further observa- 
tions of the Moon 
will show that it is 
always to be found 
in a certain narrow 
belt of stars. This 
belt is called the 
zodiac, and its cen- 
tral line is the 
ecliptic. The eclip- 



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Diag. III. 



tic is an imaginary circle which divides the whole 
sky into two equal portions, and is exactly like the 
line formed on a globe by its intersection with a 
plane passing through the centre. 

Month. — It is well worth while to verify for oneself 
that when the Moon is new, it is in the same part of 
the sky as the Sun, and that it travels round the sky 
and reaches the Sun again in one month. The length 



8 ASTRONOMY 

of the month is approximately 29J days, but varies a 
little from month to month. The times of new and 
full Moon were carefully investigated by the ancient 
astronomers for purposes of chronology. 

Meton's Cycle. — As a lunar month consists of ap- 
proximately 29J days, twelve months will contain 
approximately 354 days, and as this is 11J days short 
of the year, considerable difficulty was experienced in 
harmonizing a system of chronology depending on the 
Moon with one depending on the Sun. Meton, who 
lived between 400 and 500 B.C., discovered (if, indeed, 
the discovery is not older) that in 6940 days there 
are almost exactly 19 years, and also 235 lunar months. 
Consequently, if the dates of new and full Moon are 
known for 19 years, the same dates will serve for the 
next 19 years, and so on. A little complication arises 
in practice from the way leap years happen to fall ; 
but this cycle discovered by Meton is still the basis by 
which Christian countries fix the festival of Easter. 
As showing the accuracy attained by Meton in the 
measure of the length of a month, it may be noted 
that modern observations show that 235 months is 
about 7 J hours less than 6940 days, or that Meton's 
rule makes the month only two minutes too short. 

Observation of the Stars. — We will now make a pre- 
liminary observation of the stars. In the northern 
hemisphere the Great Bear is one of the most striking- 
constellations. Its appearance is well described by 
its American name, the Dipper. When it is once 
recognized it can always be found without any diffi- 



ANCIENT ASTRONOMY 9 

culty. Its position in the sky is different at different 
times of the night and at different times of the year. 
But it always preserves the same form; the stars do' 
not change their relative positions, but the constella- 
tion moves as a whole. 









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The character of this movement is easily seen. 
If a line be drawn, as in Diagram IV, and produced, 
it passes nearly through another star. This star, called 
the Pole Star, is always to be found by looking due 
north and (in the latitude of Great Britain) at an 
altitude of about 53 , or somewhat above the point 
midway between the zenith and the northern horizon. 
If the Great Bear be watched at intervals for a few 



IO 



ASTRONOMY 



hours it will be seen to be turning about the Pole 
Star. In the diagram its position, marked A, B, C, 
is shown at 6 p.m., midnight, and 6 a.m. on 
January i . Not only the Great Bear, but all the stars 
are seen to partake of this motion at the same rate. 
The time they take to make a complete revolution is 
evidently not very .far from a day, for on consecutive 
days at the same hour they are in nearly the same 
positions. 

If we take a constellation further from the North 



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Pole, like Orion, we find that, unlike the Great Bear, 
it cannot be seen at all times of the year. On January 



ANCIENT ASTRONOMY n 

i Orion is a little to the west of south at midnight ; 
on April i it is nearly setting in the west at midnight ; 
on July i it is not seen, and October i it is rising in 
the east at midnight. But its appearance shows no 
change, and its position is always midway between 
Aldebaran and Sirius. At whatever part of the year 
it is observed it describes the same journey in the 
sky, rising at the same point of the horizon, reaching 
the same altitude when due south and setting at the 
same point of the horizon. The stars of this constel- 
lation, like those of the Great Bear, keep at constant 
distances from the pole. 

The movement of the stars in the sky is exactly 
what we should see if we were at the centre of a 




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Diagram of Circles (VI). 

great globe on which they were fixed, and the globe 
turned about an axis pointing to the pole. Thus, 
in Diagram VI, which represents the eastern half of a 



12 ASTRONOMY 

globe, 1 1 1 is the path of a star which never sets ; 222 of 
a star which is just at such a distance from the pole 
that it rises at the north point of the horizon ; 333 is the 
path of a star still farther from the pole, which rises 
to the north of east and is above the horizon for the 
greater part of its path but below it for a shorter 
(dotted) part; 444 is the path of a star which is go° 
from the pole, and for half of its path it is above the 
horizon, for the other half below it and invisible ; 555 
shows the path of a star more than 90 from the pole, 
the part of its path during which it is above the 
horizon is less than half, and such a star rises at a 
point south of east ; 666 is the limiting path of a star 
which never rises in the latitude for which the diagram 
is drawn. 

This representation of the stars as fixed points on 
a turning sphere agrees with the facts that the stars 
do not change their relative positions, and that all 
describe parallel circles in the sky in the same time. 
This time is approximately 4 minutes less than 24 
hours. Thus each star is at the same point of its daily 
path 4 minutes earlier than it was on the preceding 
day. In a month this makes the very perceptible 
difference of two hours, and those stars which rise and 
set, rise and set two hours earlier each month. Thus 
the stars which are seen due south at midnight at 
one time of year are due south at midday after six 
months. They are not seen, owing to the glare of 
the sunlight, but that is the only reason, and with a 



ANCIENT ASTRONOMY 13 

telescope fairly bright stars may be seen in the middle 
of the day. 

The stars, then, do not change their positions in the 
sky relatively to one another, but they all move 
together like so many points pricked on a vast sphere 
which turns uniformly about an axis pointing to the 
pole. This very ancient discovery is important because 
it states these everyday phenomena of the fixed stars 
succinctly and accurately. It also furnishes us with a 
new point of view with regard to the movements of 
the other heavenly bodies, the Sun, Moon and planets. 
Instead of considering their movement across the face 
of the sky, we may consider their movements with 
reference to the stars. That the five planets, Mercury, 
Venus, Mars, Jupiter and Saturn do not remain in the 
same position relatively to the fixed stars, but wander 
among them, is very readily seen. Their motion is 
not nearly so quick as that of the Moon, illustrated 
in Diagram III, but is evident for some of them when 
their positions are compared after an interval of a 
few days, and for others after a few weeks. The 
Sun, however, presents a difficulty. Its light obscures 
the stars, and prevents a direct determination of its 
position on the celestial sphere. By carefully observ- 
ing the position of the Sun just before it sets relatively 
to Venus or the Moon, and afterwards when the night 
was dark enough for the stars to be seen, observing 
the position of Venus or the Moon relatively to the 
stars, early astronomers were able to mark the position 



H 



ASTRONOMY 



of the Sun day by day on the celestial globe. This is 
a very easy task in a modern observatory, thanks to 
the instruments we now possess for measuring angles, 
and clocks for accurately measuring time. But with 




the simple apparatus possessed by the Chaldeans, 
Egyptians and Greeks it was far from being an easy 
task. 
In the accompanying map, which represents two 



ANCIENT ASTRONOMY 15 

halves of a celestial globe on which all the brightest 
stars are marked, the position of the Sun is marked 
for the first day of each month. It will be seen that 
these positions all lie on the dotted line called the 




Diag. VII. 

ecliptic. This line is an imaginary circle dividing 
the sphere into two equal parts. It is a fixed line 
among the stars and goes through the constellations 
enumerated in the doggerel lines — 



i6 ASTRONOMY 

The Ram, the Bull, the Heavenly Twins, 
And next the Crab, the Lion shines, 

The Virgin and the Scales ; 
The Scorpion, Archer, and He-Goat, 
The Man that bears the watering-pot, 

And Fish with glittering tails. 

It is important to notice that the Sun makes this 
same journey among the stars each year and that its 
journey is intimately associated with the changes of its 
position in the sky referred to on pp. 2, 3, and illus- 
trated in Diagram I. For the circle of the ecliptic on 
the globe is in some parts nearer to the north pole 
than in others. It cuts the equinoctial or circle in the 
sky midway between the poles in two points which 
are 90 away from the poles, and half-way between 
them is, as shown in the map, 23^° nearer to or farther 
from the poles. On March 22 the Sun's position in 
the ecliptic is at one of the points where the equinoctial 
is cut. It is then 90 from the poles, and its path in 
the sky on that day is the circle DEF of Diagram I. 
The days and nights are equal, and the Sun rises due 
east and sets due west. The Sun moves along the ecliptic 
through Pisces, Aries and Taurus, and on June 22 it 
has reached a point 66J° distant from the north pole. 
During this period the days have lengthened and the 
nights shortened in the northern hemisphere. 

The converse process goes on in the next three 
months while the Sun passes through Gemini, Cancer 
and Leo, till on September 22 the days and nights are 
again equal. The Sun continues to move farther from 



ANCIENT ASTRONOMY 17 

the north for the next three months till December 22, 
when the shortest day in the northern and longest in 
the southern hemisphere occurs. It then moves north- 
ward, and on March 22 completes its circle. 

This annual movement of the Sun accounts for the 
changing of the constellations visible at night at 
different times of the year. For example, in June 
at midday Orion is in the southern sky below the Sun, 
and with a telescope the brighter stars may sometimes 
be seen, but it is in December, when the Sun is at the 
opposite part of the sky, that Orion is seen towards 
the south at midnight. 

The discovery of the movement of the Sun among 
the stars is the first great landmark in the history of 
astronomical science. The date of the discovery is 
very uncertain, and has to be inferred from slender 
evidence like the names of the constellations through 
which the Sun passes. It is probably between 2000 
and 3000 B.C. 

Eclipses of the Sun and Moon. — Eclipses of the Sun and 
Moon, especially of the Sun, are very striking pheno- 
mena. Excluding the Chinese accounts, the earliest 
eclipse of which we have any record is referred to on 
a Babylonian tablet and has been identified with one 
which occurred in 1062 B.C. Some verses in the Book 
of Amos, e.g. chapter viii., ver. 9, "to darken the 
earth while it is yet day," may be taken as an indica- 
tion that the writer had seen the total eclipse of the 
Sun which passed across Samaria on June 19, 763 B.C. 



i8 ASTRONOMY 

From the fact that Thales is said to have predicted 
an eclipse which occurred in 584 B.C., it is clear that 
considerable knowledge of these phenomena was 
possessed at that time in Ionia. But to the Baby- 
lonians belongs the honour of having discovered a 
law in these apparently very irregular occurrences. It 
was doubtless perceived soon after records were kept 
that eclipses of the Sun occurred at the time of new 
Moon, and those of the Moon at the time of full Moon. 
The correct explanation was given, viz. the inter- 
position of the Moon between the Earth and Sun in 
the case of a solar eclipse ; and the interposition of the 
Earth between the Sun and Moon in the case of a 
lunar eclipse. But as the path of the Moon among 
the stars does not coincide with that of the Sun, but is 
inclined to it at a small angle, the three bodies are 
not sufficiently in a straight line for eclipses to occur 
at every new and full Moon. The path of the Moon in 
the sky is a circle inclined at about 5 degrees to the 
ecliptic, the path of the Sun (seep. 23). The two points 
of intersection of these circles are called the nodes of the 
Moon's orbit. If the Moon is sufficiently near a node 
when it is new or full an eclipse of the Sun or Moon 
respectively will occur. From our present knowledge 
of the movements of the Moon and of its nodes — which 
move round the ecliptic in 18 years and 7 months — it 
can be shown that after 223 months the relative posi- 
tions of the Sun, Moon, and the nodes of the Moon's 
orbit will be nearly the same. Thus after this period 



ANCIENT ASTRONOMY * 9 

eclipses will recur. This very curious cycle, called the 
Saros, was discovered by the Babylonian astronomers 
from their observations of eclipses of the Moon. The 
period is 223 months or 6585*3 days, or approximately 
18 years and 11 days. If, then, the eclipses are 
recorded which occur in one period of this duration, 
those in the next period may be predicted, and so on. 
As the relationship between the numbers is not quite 
exact, an eclipse may in some cases occur which is not 
predicted by the cycle, and in some cases an eclipse 
predicted in this way may not occur, but the extreme 
cases where the rule fails from one cycle to the next 
are very few. The date of the discovery of the Saros 
cannot be fixed with" certainty, but must have been 
some centuries before the Christian era. 

The Planets. — Besides the Sun and Moon there are 
five other celestial bodies visible to the naked eye 
which move among the stars. Of these Mercury is 
only occasionally seen in Great Britain. Venus is best 
known as a brilliant evening star which is sometimes 
visible in the west about the time of sunset. At 
other times it is a morning star and rises before the 
Sun. The identity of the evening and morning star is 
said to have been discovered by Pythagoras. Venus is 
always seen in a direction not far from that of the Sun, 
the largest angle between them being 47 . The planet 
passes from side to side of the Sun as the Sun pursues 
its circuit of the sky, and when on one side is seen as 
the morning star and when on the other as the evening 
c 2 



20 ASTRONOMY 

star. Next to Venus, Jupiter is the most brilliant of 
the planets. If its position among the stars is plotted 
down each day on a celestial globe or on a map of the 
stars, it will be seen to be sometimes moving round 
the sky in the direction of the Sun's annual motion, 
but sometimes to be moving in the opposite direction. 
Its total movement in a sufficiently long interval is 
in the same sense as the Sun's motion, but the irregu- 
larities of its movement will be seen from Diagram 
VIII, giving its movement from 1908, Sept. 20, to 1909, 
July 10. Mars and Saturn exhibit a similar irregular 

movement among 
the stars. The 
most important dif- 
ference between the 
movements of these 
three planets is that 
Mars takes 2 years, 
Jupiter 12 years and Saturn 29J years to complete the 
circuit of the sky. 

The Greek astronomers succeeded in expressing the 
observed movements of the planets, as well as of the 
Sun and Moon, by mathematical formulas, so that 
their position could be calculated and predicted. This 
was an immense step in the progress of astronomy. 
A formula, however empirical it may be, which cor- 
rectly represents the facts, simplifies their statement 
and brings them into orderly arrangement and small 
compass. As an example we may take the representa- 





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XII XI 

Diacr. VIII. 



ANCIENT ASTRONOMY 



21 




Diag. IX. 



tion of the movement of Jupiter as given by the Greek 
geometricians. 

Let the point I in Diagram IX make the circuit of 
the sky in 12 years. Represent this by the movement 
of I round the circumfer- 
ence of the circle whose 
centre is E. Meanwhile 
let the point J move round 
a circle of \ the radius of 
EI in the course of one 
year. As seen from E, 
J when at ] ± will be 
moving in a retrograde 
direction, when at J 2 in a 
forward one. This epi- 

cyclic movement of I as seen from E presents the 
main features of the movement of Jupiter among the 
stars, namely, its alternate progression and retro- 
gression. Further, by taking the radii of the circles 
and the periods in which they are described in suitable 
proportions, the movement of J in the diagram as seen 
from E agrees in amount with the observed motion 
of Jupiter in the sky. 

Hipparchus. — Hipparchus, one of the greatest of all 
astronomers, lived at Rhodes, and made observations 
between 146 and 126 B.C. He invented trigonometry, 
and by its aid made geometrical representations of the 
motions of the heavenly bodies by means of epicycles, 
eccentrics, etc., in dose numerical agreement with the 



22 



ASTRONOMY 



best and most detailed observations which were then 
possible. For example, it was known that the Sun 
moved across the sky more rapidly in winter than in 
summer. Hipparchus showed that the movement would 
be accurately represented if the Sun moved uniformly 
round the circle whose centre is O (Diagram X), but the 
earth from which it is seen had the slightly eccentric 
position E. He fixed the position of E as being Y Vth 

part of the radius distant 
from O, and in such a 
direction that the Sun was 
at A on June i. 

Hipparchus made a 
great step in unravelling 
the motion of the Moon, 
which, when observed in 
detail and with accuracy, 
is extremely complicated. 
As in the case of the Sun he found that its varying 
rate of motion could be represented by supposing the 
Earth to be placed eccentrically in a circle whose 
circumference was uniformly described by the Moon . He 
discovered that to represent the motion accurately the 
line corresponding to EA of the last diagram revolves 
in a time which he fixed at 9 years. This is known as 
the movement of the apse. He also determined the 
inclination of the Moon's orbit to that of the ecliptic 
to be 5 , and showed that the points where the circle 
which the Moon traced on the celestial sphere cut the 




Diag. x. 



ANCIENT ASTRONOMY 23 

ecliptic are not fixed but move round in a period 
of 19 years. Thus in Diagram XI, if N 1 AM 1 B is the 
ecliptic, and N 1 CM 1 D the Moon's orbit; the angles 
at N x and M ± were found to be 5 ; and the points N x , 




Diag. XI. 

M 1 carrying the circle N 1 CM 1 D with them moved 
round N 1 AM 1 B in 19 years. 

Perhaps the most famous of the discoveries of 
Hipparchus is that of the precession of the equinoxes. 
In the year 134 B.C. the appearance of a new star 
in the constellation Scorpio led Hipparchus to make 
a catalogue of 1080 stars for comparison with cata- 
logues made at other dates. He determined the posi- 
tion of the stars with all possible precision. When 
he compared this catalogue with earlier ones he found 
that the stars had shifted their positions with reference 
to the equinoxes or points in the sky where the ecliptic 
cuts the equinoctial. As the stars all showed the same 
shift, the change in their positions was attributed by 
him to a movement of the equinoxes in an opposite 
direction, 



24 ASTRONOMY 

The meaning of this discovery will be understood 
more clearly by reference to the map on pp. 14, 15. 
The ecliptic or path of the Sun among the stars does 
not change ; its course is through the constellations of 
Aries, Taurus, etc. But in the map it will be seen 
that the Sun is midway between Pisces and Aquarius 
at the time when it crosses the equinoctial, i. e. at 
the time in spring when the Sun is just 90 from the 
pole and the days and nights are equal. In the time 
of Hipparchus the equinoctial was in a different posi- 
tion and cut the ecliptic at a point in the constellation 
Pisces, 28 from its present position. The equinoxes 
move round the ecliptic in 26,000 years, a move- 
ment discovered by Hipparchus by the differences be- 
tween his catalogue and one constructed 150 years 
previously. Now the pole of the sky bears the same 
relation to the equinoctial as the pole of the Earth does 
to the Equator, being 90 away from every part of it. 
As the equinoctial moves the pole necessarily moves 
too, and thus precession states that the point of the 
sky about which the stars turn slowly changes its 
position, describing among the stars in 26,000 years 
a small circle whose radius is 23J . At present the 
pole is near the star Polaris. Its positions 6500 years 
ago and 13,000 years ago are shown on the map. 

The effect of the precession of the equinoxes is to 
change the time of year at which the constellations 
are visible. Orion is at present a winter constellation. 
We see it due south at midnight in December, 6ooo 



ANCIENT ASTRONOMY 25 

years ago it was due south at midnight in the 
autumn. In 6000 years more it will be due south at 
midnight in the spring. These changes brought about 
by precession in the positions of the stars in relation 
to the seasonal changes of the Sun can be in some 
instances used for chronological purposes. For 
example, Hesiod gives information about the times of 
rising and setting of Sirius at certain times of the 
year — the year being defined by the seasons — which 
can be used to verify the approximate date at which 
he wrote. The approximate dates of some of the 
pyramids and some temples have been determined by 
more or less conjectural relationships between the 
position of the Sun and some bright star at the time 
of their erection, the rising of the star having been 
used as a warning of the approach of sunrise at the 
equinox or at midsummer's day. 

The Distance of the Sun, Moon, and Planets. — That 
the Earth is a sphere was believed by Plato and 
Aristotle. Their reasons were the same as those given 
in modern books on geography, except the reason 
which might be expected to convince even the least 
reflective, namely, that people have been round it and 
nearly all over it. Eratosthenes, the librarian at Alex- 
andria, who lived from 276 to 196 B.C., first determined 
its size. He observed that at the summer solstice the 
Sun was vertically overhead at Syene in lower Egypt, 
but at Alexandria made an angle with the vertical of 
7t° or-^th part of the circumference of a circle. 



26 



ASTRONOMY 




Taking the Sun to be at a distance so much greater 
than the distance AS, Diagram XII, that the lines 

from A and S to the Sun are 
parallel, the angle AOS be- 
tween the verticals at the two 
places is 7^°. Thus AS : 
Circumference of Earth = 
7i°: 3 6o°=i: 50. 

The distance between 

Syene and Alexandria was 

measured and found to be 

5000 stadia, and therefore the 

circumference of the earth 

was 250,000 stadia. The 

iag * 1L value of a stadium is not 

known exactly, and the accuracy of the result cannot 

be stated, but the method is sound and the result not 

far from the truth. 

Knowing the size of the Earth Hipparchus was 

able to measure the distance 
of the Moon. When the 
Moon is partially eclipsed 
the edge of the shadow of 
the Earth is seen as part of 
a circle on the Moon, as in 
Diagram XIII. The size of 
this circular shadow is com- 
pared with the size of the 
Moon. The apparent diameter of the Moon is J° or 
30 7 ; thus it is found that the shadow of the Earth at the 




Diag. XIII. 



ANCIENT ASTRONOMY 27 

distance of the Moon subtends an angle of 8o'. Dia- 
gram XIV, in which S, E, M are the Sun, Earth and 

F 




Diag. XIV. 

Moon, shows how the shadow is formed. The angle 
AEB is thus found to be 8o r , while the angle FEG 
under which the Sun is seen is 30' - 1 [In the diagram 
these angles are necessarily grossly exaggerated.] 

With these data, and making the assumption that 
the Sun's distance is 20 or 30 or any large number of 
times the Moon's distance, Hipparchus found that the 
Moon's distance from the Earth was about 59 times 
the radius of the Earth, and that the result did not 
vary much with the different hypotheses made as to 
the Sun's distance provided it was a good many times 
larger than that of the Moon. 

Ptolemy, who lived at Alexandria about a.d. 150, 
determined the distance of the Moon by a method 
which is substantially the one now adopted. If at 
the same moment the position of the Moon be observed 
from two places A and B at a considerable distance 
apart on the earth (Diagram XV); and ZAM, YBM, 

1 The angle through which we turn in looking from one 
direction to a perpendicular one is called a right-angle. If this 
angle is divided into 90 equal parts, each is called one degree, and 
written i°. One-sixtieth part of a degree is called a minute, and 
written 1'. One-sixtieth part of a minute is called a second, 
and written 1". 



28 ASTRONOMY 

the angles between the directions of the Moon, and 
the verticals at the two places be measured; knowing 
the positions of A and B on the Earth's surface, it 
is possible to draw the diagram below to scale and 
thus infer how large OM, the distance of the Moon, 




Diag. XV. 

is as compared with OA or OB, the radius of the 
Earth. In actual practice trigonometrical calcula- 
tions are used, but that is only because drawing to 
scale cannot be done with sufficient accuracy. 

The Moon's distance was thus satisfactorily deter- 
mined, and Ptolemy tried to use his result in com- 
bination with the eclipse method of Hipparchus to 
obtain the Sun's distance. He found that the Sun 
was 20 times as far away as the Moon. This is much 
too small ; we know now that the Sun is nearly 400 
times as far away as the Moon. The method used by 
Ptolemy is not susceptible of giving the Sun's distance 
with accuracy. 

The Almagest. — Although Ptolemy made several 
discoveries of very great importance, the greatest 



ANCIENT ASTRONOMY 29 

service he rendered to astronomy consists in his 
treatise, jxeya\y] (Tuvra^is, or the Almagest, as it was 
called later by the Arabian astronomers. This work 
contains the whole body of astronomical knowledge 
then known, and was for 1400 years an astronomical 
bible. 

The preceding pages give some idea of the im- 
mense progress made by the Greeks in astronomy. 
They had reached correct ideas of the shape and size 
of the Earth and the distance of the Moon ; they knew 
that the Sun was much farther away than the Moon, 
and guessed from the rates of movement of the planets 
round the sky that their distances were of a. similar 
order of magnitude, Jupiter and Saturn being the 
most distant, while the fixed stars were much farther 
away. Again, the movements of Sun, Moon and 
planets had been studied in considerable detail, and 
geometrical and trigonometrical representations of 
them had been devised. These representations were 
sufficiently accurate for the prediction of their positions 
and of eclipses. In these geometrical representations 
the Earth was taken as stationary, and movements attri- 
buted to the Sun, Moon and planets and the celestial 
sphere of the stars. It may well be that Hipparchus 
and Ptolemy regarded as formulas what their more 
ignorant successors regarded as dogmas. In any case 
the skill with which the movements of the heavenly 
bodies were traced and brought into relationship with 
geometry made astronomy an exact science of great 
scope and interest. 



CHAPTER II 

THE COPERNICAN SYSTEM 

Copernicus. — From Ptolemy's Almagest in the 
middle of the second century, to the De Revolutioni- 
bus of Copernicus in the middle of the sixteenth 
century, comparatively little progress was made in 
astronomy. But the publication of the De Revolu- 
tionibus in 1543 was the beginning of a new astro- 
nomical era. The 1 change from the ancient to the 
modern conceptions of astronomy is associated with 
four great names — Copernicus, Galileo, Tycho, and 
Kepler. 

Copernicus stated two propositions — 

(1) That the diurnal movement of the stars is appar- 
ent only, and results from a rotation of the Earth about 
its axis in the opposite direction. 

(2) That the Earth is one of the planets, and, like 
them, revolves round the Sun. 

These are the commonplaces of modern astronomy ; 
it is, however, both interesting and important to 
notice the arguments which were adduced in their 
favour, and those brought against them. 

Earth's Diurnal Rotation. — Copernicus showed clearly 
the relative character of motion. The apparent motion 

30 



THE COPERNICAN SYSTEM 31 

of objects as seen from the window of a railway car- 
riage is so familiar that it is not necessary to elabor- 
ate the proposition that the appearance of motion is 
equally produced by a movement of the object or 
the observer. The apparent movement of the stars in 
parallel circles is identical with the movement which 
would be produced by a rotation of the Earth about 
its axis. The objections are, the difficulty of believ- 
ing in the motion of so large a body as the Earth ; 
that we should be entirely unconscious of this move- 
ment; and that movable bodies, specially the air, 
should not be left behind. Copernicus points out 
that these objections would apply with far greater 
force to a rotation of the celestial sphere containing 
the stars, for this is immeasurably larger than the 
Earth, and would need to move at an immeasurably 
greater speed to accomplish a diurnal rotation. 

Annual Revolution of Earth round the Sun. — The 
annual motion of the Sun among the stars is as 
well explained by an annual revolution of the Earth 
about the Sun as by that of the Sun about the Earth. 
In Diagram XVI, when the Earth is at E, the Sun 
will appear projected against the sky at e ; when the 
Earth moves to F, the Sun will appear projected 
against the sky at /, and the appearance of the Sun's 
annual movement among the stars will be produced. 

The explanation of the seasons offers no difficulty. 
The axis round which the Earth makes its daily 
rotation is fixed in a direction not perpendicular to 



32 ASTRONOMY 

the plane in which the Earth revolves round the Sun, 




Diag. XVI. 

but inclined at 23J to this perpendicular. In Dia- 
gram XVII the centre of the Earth describes the 




Diag. XVII. 

circle CCCC about the Sun in the direction shown by 



THE COPERNICAN SYSTEM 33 

the arrows. As the axis is not perpendicular to the 
plane of this circle, in June the northern hemisphere 
is more directly under the Sun's rays, or the Sun 
appears higher, being directly overhead at a point 
north of the equator. Similarly, in December the 
point on the Earth where the Sun is directly over- 
head is south of the equator. By running a knitting- 
needle through a ball of worsted a model can be con- 
structed, with which the movement of the Earth round 
the Sun can be imitated, and the cauVe of the Earth's 
seasonal changes explained. 

The alternations of forward and retrograde motion 
of the major planets (see p. 20), which is repre- 
sented by an epicyclic motion on the Ptolemaic 
system, is accounted for at once by Copernicus. The 
movement of Jupiter, for example, is represented in 
Diagram IX by a movement of I round E (the Earth) 
in twelve years, w<hile J (Jupiter) moves round I in one 
year. Diagram XVIII 
shows how this would be 
represented on the Coper- 
nican system. S is the 
Sun; E, the Earth, de- 
scribes a circle round it in 
one year, J, Jupiter, de- 
scribes a circle round S in 
twelve years, the radius 
being five times SE. If iag " 

the line EI is drawn parallel to SJ and J I parallel to 




34 ASTRONOMY 

SE, then the points I and J bear the same relation to 
E as in the Ptolemaic diagram, for EI and IJ are 
equal in length and in the same directions in the two 
diagrams. Thus in the Copernican system the ap- 
parent motion of Jupiter relatively to the Earth, or 
as seen from the Earth, is shown to result from a 
motion of Jupiter round the Sun in a circle, com- 
bined with a motion of the Earth — the point from 
which Jupiter is viewed — in another circle. 

The essential features of the movements of the 
planets Venus and Mercury are readily explained. 
As they move round the Sun in less than a year, they 
will necessarily be seen from the Earth first on one 

side and then on the other 
side of the Sun. In Dia- 
gram XIX, if Venus is at V 
when the Earth is at E, 
looking at the Sun from E, 
Venus would appear on the 
left hand, while if the Earth 
reaches E ; when Venus 
reaches V 7 , it will be seen 
iag * ' on the right hand. Thus 

Venus will be alternately a morning and evening star, 
and can never be more than a certain angular distance 
from the Sun, as it will always be within the angle 
formed by the two tangents from the Earth to the 
circle along which Venus moves. 

Copernicus further showed how the relative dis- 




THE COPERNICAN SYSTEM 35 

tances of the planets from the Sun could be obtained. 
As Mercury never gets so far from the Sun as Venus, 
it must describe a smaller circle ; the knowledge of 
the greatest angle its direction can make with that 
of the Sun makes it possible to draw this circle to 
scale with the one described by the Earth. Similarly 
with regard to Venus, if EK is drawn so that SEK 
is the greatest angular distance Venus attains from 
the Sun, it is only necessary to draw a circle with 
centre S to give the orbit of Venus. The distances 
of Mars, Jupiter and Saturn are deducible from the 
extent of their retrograde motions. Thus Copernicus 
was able to draw a plan of the solar system, giving the 
planets in their order of distance from the Sun, and 
at their proportionate distances. He pointed out that 
this order agreed with the order which could be 
inferred from their times of revolution. Thus Mer- 
cury, the nearest, goes round the Sun in 88 days, 
Venus in 223 days, the Earth in a year, etc., and 
Saturn, the most distant, in 30 years. Diagram XX, 
taken from the De Revolutionibus, gives the order, 
but not the correct relative distances. It will be 
noticed that the Moon revolves round the Earth as in 
the Ptolemaic system, and is carried with the Earth 
in its orbit round the Sun. 

Difficulties of Copernican System. — The Copernican 
system presented several difficulties. How the Moon 
could be carried round the Sun with the Earth is a 
mechanical problem which was not at that time 



d 2 



36 ASTRONOMY 

soluble. Another objection arose from the absence 
of any appreciable motion of the fixed stars. Their 
immense distances are familiar to us now, but at the 
time when the Copernican system had to meet 
criticism their distances might well have been sup- 
posed to be 10, or 20, or 30 times the distance of 




Diag. XX. 

Saturn. If the Earth described a circle round the 
Sun, its positions when on opposite sides are a very 
great distance apart. It was to be expected that the 
stars, seen from two points so far apart, would show 
some differences of relative position. The only reply 
which could be given — and it is the correct one — was 
that the distances of the fixed stars are so great that 
the distance between the Earth and Sun is inappre- 
ciable in comparison with them. 



THE COPERNICAN SYSTEM 37 

Other objections to the Copernican system were its 
supposed opposition to the Bible and its disagreement 
with the orthodox astronomy found in the writings 
of Ptolemy and Aristotle. Curiously enough the 
authority of Greek teachers was its greatest obstacle, 
although freedom of thought is a heritage the world 
owes so largely to Greek philosophy. It was a 
hundred years before the Copernican system com- 
pletely superseded that of Ptolemy. 

Galileo. — Galileo supported the Copernican theory 
by arguments which appealed to a wider audience 
than the mathematical treatise of Copernicus. In 
1609 he learned, that a Dutch optician had by a com- 
bination of lenses devised an instrument which made 
distant objects seem near. Galileo realized the optical 
principles which must underlie such an instrument, 
and soon made one himself which magnified thirty 
times. He pointed this to the sky, and found that the 
number of stars visible was much greater than could 
be seen with the naked eye. 

Seen in his telescope the Moon presented the 
appearance of a mountainous country with dark 
shadows cast by the mountains. Near the edge 
between the bright and dark parts he saw bright spots 
where the mountain tops were illuminated by the 
rising or the setting sun, while the valleys were still 
in darkness. From the lengths of the shadows he 
calculated the heights of the mountains. Some of 
the dark parts he erroneously supposed to be water. 



38 



ASTRONOMY 



Thus the Moon, instead of being a crystal globe, as 
the old astronomers believed, had mountains and 
valleys like the Earth. 

Pointing his telescope to the planets he found that 
they were not bright points like the stars, but discs of 
sensible magnitude like the Sun and Moon. The 
appearance of Venus was especially striking. It was 
seen to have phases like the Moon, and the conclusion 
was irresistible that, like the Moon, it shines by the 
reflected light of the Sun, and not by its own light. 
y .„ ,„ t , ^ , wi This established a resem- 
blance between Venus and 
the Moon, and afforded 
another argument in favour 
of the Copernican theory. 

On January 7, 1610, he 
saw three small stars in a 
line with Jupiter (Diagram 
XXI). By accident he 
examined Jupiter again on 
January 8, and found them 
in a different position. 
January 9 was cloudy. On 
January 10 he found two 
stars both on the east of the 
planet. On the nth he 
found two on the east, but 
the most easterly one was much the brighter. On 
the 1 2th he saw three stars, the third one emerging 



; - Oh. 


O * * * 


Oca 


On, 


* *o 


Occ» 


On. 


* * 


Osd, 

. ■ o«;.,' 


Or... 




■ 


■-Orti 


* * * 


■-. j 



Diag. XXI. 



THE COPERNICAN SYSTEM 39 

from behind the planet during his observations. On 
the 13th he saw four stars. Galileo perceived that 
these stars were four satellites revolving round Jupiter 
just as the Moon revolves round the Earth. He 
observed them further, and determined their periods 
of revolution. The analogy between Jupiter and his 
satellites and the Earth and Moon was another argu- 
ment for the Copernican theory. As Jupiter's moons 
revolve around and accompany Jupiter, may not 
the Earth's Moon accompany the Earth in its revolu- 
tion about the Sun ? 

Galileo's telescope revealed to him still another 
analogy which lent support to the Copernican theory. 
He discovered spots on the Sun which did not remain 
stationary, but crossed the disc in fourteen days, and 
showed changes in appearance which, as he explained, 
would naturally arise from perspective when the spots 
were seen at an increasing angle. He concluded 
that the Sun rotated on an axis. If the Sun, why 
not the Earth ? 

In 1632 Galileo published his great work, the 
Dialogue on the Two Chief Systems of the World — 
the Ptolemaic and the Copernican. The arguments 
in favour of the Copernican system were put forward 
with unanswerable force, and the book was received 
with applause all over Europe. Unfortunately for 
Galileo, he had made many enemies during a life 
full of controversy. They procured his trial by 
the Inquisition, and he was compelled to abjure 



4 o ASTRONOMY 

his opinions. But, although his book was condemned, 
the Copernican system was effectively established. 

There can be no question of the important part 
which Galileo's telescope played in the substitution of 
a system of the world with the Sun as centre (helio- 
centric) for the Ptolemaic one in which the Earth 
was the centre (geo-centric). Copernicus put the 
geometrical arguments with great force in the De 
Revolutionibus, but he had no new facts to bring 
forward. A heliocentric theory had been previously 
proposed by the Greek astronomer Aristarchus, and 
the Babylonian astronomer Seleucus is said to have 
nearly convinced Hipparchus of its truth. Galileo's 
telescope transformed the planets from bright points 
into worlds, and thus added a force to the arguments 
of Copernicus which made them irresistible. 

Tycho Brahe. — The Copernican system satisfied the 
observed planetary motions in broad outline, but for 
more accurate representation it was necessary to add 
a number of small epicyclic or eccentric movements. 
In 1546, a few years after the death of Copernicus, 
Tycho Brahe was born. Tycho became a great astro- 
nomical observer as contrasted with a theorist. The 
multitude and accuracy of his observations of the Sun, 
Moon and planets were destined to furnish the key by 
which the Copernican system was freed from the 
numerous subsidiary epicycles, etc., and the true 
movements of the planets discovered. Apart from 
particular discoveries, such as his determination that 
the comet of 1577 was more distant than the Moon, 



THE COPERNICAN SYSTEM 41 

and revolved round the Sun, Tycho's services to 
astronomy consist in the great improvements he made 
in astronomical instruments and in the accuracy of 
observations. He used his instruments with great 
skill, and also realized the importance of making long 
series of continuous observations. 

Kepler. — Tycho's observations of Mars passed into 
the hands of his pupil and successor, Kepler, who, 
unlike his master, was a Copernican. For two 
reasons Mars is the most difficult of the planets 
for which to construct tables in harmony with the 
observations. As Mars sometimes comes near the 
Earth, its movements can be determined with great 
precision and any irregularities become apparent. 
Besides this, the orbit of Mars diverges more from 
the circular form than that of any of the other planets. 
A very complicated geometrical system of epicycles 
and eccentrics (pp. 21, 22) is required in order to 
represent the motion in satisfactory accordance with 
the facts. 

Kepler tried hypothesis after hypothesis, but could 
not by systems of epicycles represent Tycho's obser- 
vations with sufficient accuracy. He then tried other 
forms of curves, a daring innovation, as it was univers- 
ally believed that the celestial motions must be com- 
posed of circular movements. Each different hypo- 
thesis involved an immense amount of labour, as all 
the calculations had to be started anew, and in Kep- 
ler's time there were no logarithm tables or other 
modes of simplifying numerical work. Finally, Kepler 



4 2 



ASTRONOMY 




Diag. XXII. 



tried the ellipse, and found that with the Sun in 
one of the foci he could adequately represent Tycho's 
observations. The ellipse is the curve which is ob- 
tained when a cone is cut obliquely. It may also be 
considered as the curve which a point P describes if 
it moves so that the sum of its distances from two 

points, S and H, re- 
mains the same. The 
two points S and H 
are called the foci. 
If they are a long 
way apart the ellipse 
is elongated or very 
eccentric ; if close to- 
gether it approaches more nearly to a circle. But 
Mars does not move uniformly in this ellipse, its 
velocity being greater when it is near the Sun than 
when it is further away. Kepler discovered how the 
velocity varies at different points in the planet's orbit. 
Kepler's Laws. — The results were stated in what are 
known as Kepler's first and second laws of planetary 
motion. 

i. The planets move in ellipses having the Sun in 
a focus. 

2. The straight line joining a planet to the Sun 
sweeps out equal areas in equal times. 

Thus in Diagram XXIII a planet will describe the 
large angle A'SP 7 in the same time as the small angle 
ASP, because the area A ; SP ; equals the area ASP. 




THE COPERNICAN SYSTEM 43 

These famous laws were published in 1609. They 
were first established for Mars, 
and in course of time for the 
other planets, and even for 
the satellites which Galileo 
had found to circulate round 
Jupiter. 

In 1619 Kepler discovered a third law which shows 
the relationship between the distance of a planet from 
the Sun, and the time it takes to perform a complete 
revolution. The more distant the planet the longer its 
period of revolution, but the planets do not move at 
the same rate : e.g. Jupiter is five tines as far away 
from the Sun as the Earth, but takes twelve years, 
not five years, to complete its revolution. 

Kepler's third law is — 

The square of the time of revolution of any planet 
about the Sun is proportional to the cube of its mean 
distance from the Sun. 

The meaning of this law will be clearly seen by in- 
spection of the following table, in which a is the mean 
distance of a planet from the Sun, the Earth's mean 
distance being taken as 1, and T is the time in years of 
its revolution. 





Mercury 


Venus 


Earth 


Mars 


Jupiter 


Saturn 


a 


•387 


723 


I 


i'5 2 4 


5*203 


9-539 


(fi 


•058 


•378 


I 


3 '54 


140*8 


868 -o 


T 


•241 


•615 


I 


1 -88 1 


n-86 


29-46 


T 2 


•058 


•378 


I 


3*54 


1407 


8679 



44 ASTRONOMY 

The agreement of the figures in the second line with 
the corresponding figures in the fourth line constitutes 
the third law. 

The Ptolemaic astronomy gave geometrical repre- 
sentations of the apparent movements of the heavenly 
bodies. The Copernican system gives their real move- 
ments. Kepler's laws, substituting the ellipse for the 
circle, gives these real movements with all the accuracy 
that Tycho Brahe's refined observations demanded, 
and are a concise statement of all the apparently 
complicated facts of planetary motion, as far as they 
had at that time been elicited by observation. 



CHAPTER III 

THE LAW OF GRAVITATION 

Movement of Bodies in Curved Paths. — The science of 
dynamics, which may be said to have been founded 
by Galileo, led to further inquiry into the elliptic 
motion of the planets. Galileo investigated the 
motion of falling bodies on the Earth, and Huyghens 
showed under what conditions a body could revolve 
uniformly in a circle. Put very roughly, the con- 
dition is that the tendency to fly off should be counter- 
acted by a pull towards the centre. For the Moon to 
revolve uniformly round the Earth in a circle, it is 
not necessary that it should be pushed in the direc- 
tion of its motion, but it is necessary for it to be 
constantly pulled towards the Earth, otherwise it 
would move in a straight line. Since bodies on the 
Earth fall to the ground however high we may go, 
the Earth may be regarded as exercising an attractive 
force upon them. Might not this force continue to 
act, though to a diminished amount, at the distance 
of the Moon ? Newton put this question to himself, 
and answered that if the attraction diminished accord- 
ing to the inverse square of the distance from the 

45 



46 ASTRONOMY 

Earth's centre, the Moon would move round the 
Earth in the circle it actually describes. As the 
Moon's distance is 60 times the Earth's radius, the 
diminution of the attraction according to the inverse 
square of the distance from the Earth's centre means 
that the attraction on a body at the Earth's surface 
would be diminished (-^V) 2 at the Moon's distance. 
Newton compared the motion of the Moon to that of 
a bullet fired from the top of a hill. One fired 
horizontally from A with small velocity reaches the 

Earth at B ; a 
second, fired 
with greater 

velocity, at C ; a 
third at D. If 
Diag. xxiv. the bullet could 

be fired with sufficient velocity it would not fall to 
the Earth, and if the velocity were exactly the right 
amount, the bullet would move round the Earth in a 
circle. 

Movement in Ellipses. — Under what conditions will 
the planets describe ellipses round the Sun in accord- 
ance with the laws discovered by Kepler ? Newton 
was able to answer this question fully. From the 
second law, that equal areas are swept out in equal 
times, he proved that the planets were subjected to 
attractive forces drawing them towards the Sun. 
From the fact that the path of a planet is an ellipse 
with the Sun in a focus, he showed that this force 




THE LAW OF GRAVITATION 47 

varies inversely as the square of the planet's distance 
from the Sun. From Kepler's third law he showed 
that the Sun's attraction is the same for all the planets, 
the amount depending only on the inverse square of 
each planet's distance from the Sun. 

Law of Gravitation. — In this way Newton was led 
to propound the law of universal gravitation that 
every particle of matter attracts every other with a 
force which is proportional to the mass of each and 
inversely proportional to the square of the distance 
between them. Thus, if at A there is a particle of 

matter whose mass is M, > ^ 

and at B another whose A 3 

a •£ +u v Diag. XXV. 

mass is m, and 11 the dis- 
tance AB be called r, then each particle exerts on 
the other an attractive force which is proportional to 

M x m T , , , .. 1 

2 — . it does not matter what the particles are 

made of, or whether they are both on the Earth or 
both in the Sun, or one on the Earth and the other 
on Sun, Moon, or planets. 

Consequences of Law of Gravitation. — Newton now 
put forward the law of gravitation as an hypothesis 
whose consequences are to be deduced and compared 
with the observed phenomena of the solar system. 
Its immense range is seen from the variety of these 
consequences. Not only the movements of the Moon 
and planets, but the shape of the Earth and the 
planets, the ebb and flow of the tides and the preces- 



4 8 ASTRONOMY 

sion of the equinoxes, were shown by him to be dedu- 
cible mathematically from the law of gravitation. The 
verification of this law became one great branch of 
astronomy. Irregularities in the lunar and planetary 
motions have constantly presented new problems, 
which have been resolved as due to some consequence, 
till then unrecognized, of universal gravitation ; while, 
on the other hand, the law has been confidently used 
to determine the condition of the solar system in past 
and future times. 

Attraction of Spheres. — The total attraction of one 
body on another is made up of the attractions of each 
particle of one body on each particle of another. 
These are in varying directions and of various 
amounts. Newton w r as able to prove mathematically 
that spheres of uniform material or made up of con- 
centric shells of uniform material attract one another 
just as if their masses were concentrated at their 
centres. This proposition would naturally be ex- 
pected to hold for two spheres whose distance apart 
was much greater than their radii. Newton showed 
that it holds for all distances, and was thus able to 
calculate the combined effect of the attractions of all 
the particles which compose the Earth on a body at 
its surface, and thus verify that the law of universal 
gravitation gives a correct relationship between the 
attractive force observed in falling bodies at the 
Earth's surface, and that required to keep the Moon 
in its orbit. 



THE LAW OF GRAVITATION 49 

Shape of the Earth. — In an expedition to Cayenne, in 
South America, near the equator, a French astrono- 
mer, Richer, found that a pendulum swung more 
slowly there than in Paris, thus showing that the 
force of gravity is less at the equator than in the 
latitude of Paris. Newton proved that this result 
necessarily follows from the law of gravitation, and 
that the Earth bulges out somewhat from the spherical 
form at the equator. If this were not the case, the 
water of the ocean would, owing to the Earth's spin, 
tend to flow towards and heap itself up near the 
equator. 

Tides. — Newton also gave a general explanation of 
the tides. The solid Earth, by virtue of its rigidity, 
responds to the attraction of the Moon en masse. But 
the actual attractive force varies somewhat from place 
to place according to the distance from the Moon. 
The result is that when the mean effect of the Moon's 
attraction is abstracted, there remains a force which 
tends to raise tides on the side of the Earth facing the 
Moon and also on the opposite side. The mobile water 
yields to this tide-producing force, whereas the Earth's 
rigidity prevents it from giving, and the water moves 
relatively to the Earth, producing tides. The occur- 
rence of two tides a day is thus explained, for the 
water tends to rise at the points nearest to and farthest 
from the Moon, and as the Moon takes 50 minutes 
more than the 24 hours to complete its apparent re- 
volution round the Earth, the time of high water is 



5 o ASTRONOMY 

50 minutes later each day. The attraction of the Sun 
also produces tides, but only half as large as those 
produced by the Moon. At New and Full Moon 
the forces exerted by the Sun and Moon combine, 
and spring tides occur, while when the Moon is in a 
direction at right angles to the Sun, their tide-pro- 
ducing forces are opposed, and neap tides result. 

Precession of the Equinoxes. — The precession of the 
equinoxes, interpreted in the light of the Copernican 
system, means that the axis round which the Earth 
spins is not fixed in direction, but slowly changes. 
In 26,000 years it describes a cone whose axis is'per- 
pendicular to the ecliptic; the angle between the axis 
of the Earth and the axis of the cone is always 23J . 
In Chapter I this was expressed slightly differently, 
when it was said that the pole described a small circle 
of radius 23J among the stars in 26,000 years. 

Newton showed that this motion of the Earth's 
axis is a consequence of its oblate figure. In order 
to see the effect of the attraction of the Sun and Moon 
on the Earth, consider separately the sphere which 
can be just enclosed in the Earth, and the oblate part 
which bulges out at the equator. The attraction of 
the Sun, for example, on the spherical part produces 
a pull in the direction OS (Diagram XXVI), but does 
not tend to turn the Earth. The attraction on the 
nearer half of the part bulging out at the equator 
produces a pull in a direction ES, while the attraction 
on the more distant half produces a pull in the direc- 



THE LAW OF GRAVITATION 



5i 




tion E'S. But as E is nearer to S than E 7 , the pull 
along ES is greater than that along E 7 S, and there 
result forces which tend to right the Earth, or bring 
OP nearer to OK. But 
when the dynamical con- 
sequences of this righting 
force are investigated, it 
is found that owing to the 
Earth's spin, the axis 
OP, instead of being 
moved nearer to OK, Dia ^ > :vL 

keeps at the same distance, but slowly describes a 
cone around it. This result may at first sight appear 
paradoxical, but a similar result 
from similar causes is familiar in 
the peg-top : while the top spins 
round its axis, the axis describes a 
cone about a vertical line and the 
top does not fall down as it would 
if it were not spinning. 

Comets. — The ellipse is not the only curve which 
a body can describe about another to which it is 
attracted by a force varying inversely as the square 
of the distance. If a cone be cut perpendicularly to 
its axis, we get a circle; if the plane is not quite 
perpendicular, we get an ellipse; as the plane of 
section becomes more inclined to the axis of the cone 
the curve becomes more and more elliptic, till when 
the plane is parallel to an edge of the cone the curve 
e 2 




PEGTOP. 



Diag. XXVII. 



52 



ASTRONOMY 



is no longer closed, but becomes an open curve called 
a parabola, and at still greater divergence of the cut- 
ting plane from perpendicularity a curve called a 
hyperbola. The forms of these curves are shown in 
Diagram XXVIII. All these conic sections are 

possible paths for a body 
to describe about the Sun 
under the influence of 
gravitation. The planets 
describe nearly circular 
orbits. Newton showed 
that comets move in ellip- 
tic orbits of great eccen- 
tricity or in parabolic 
orbits. Thus comets are 
brought into the scheme of 
the solar system, and are 
seen to move like the 
Earth and planets under 
the dominating influence of the Sun's attraction. 

Masses of Heavenly Bodies. — A very interesting con- 
sequence of the law of gravitation is its application 
to determine the masses of heavenly bodies. If the 
mean distance between two bodies whose masses are 
M and m is a, and they revolve about one another in 

a s 
the time T, then the quantity ™ is proportional to 

Mi + ra, the sum of the two masses. By taking a to be 
the Moon's mean distance, and T the time in which 




Diag. XXVIII. 



THE LAW OF GRAVITATION 53 

the Moon revolves, the formula may be applied to the 
Earth and Moon. By taking a to be the Sun's mean 
distance and T the year, it may be applied to the Sun 
and Earth. The Sun's distance is, let us say, 390 times 
that of the Moon, and the year is, roughly, 13 times 
as long as a sidereal revolution of the Moon. The 
combined mass of the Sun and Earth is, therefore, 
greater than that of the Earth and Moon in proportion 

of ^— . Thus the Sun's mass is 3=^0,000 times that 
i3 2 

of the combined mass of the Earth and Moon. By 
taking a to be the distance of one of Jupiter's 
satellites and T the time in which it revolves round 
Jupiter, the formula is applicable to determine the 
mass of Jupiter. This is the astronomical method of 
determining the masses of the heavenly bodies. 
They are measured by the attractions they exert on 
one another, and these attractions are proportioned 

to ™. The method has been applied to all the 

planets which have satellites and to double stars, 
when the distance between the two stars can be 
determined. 

Disturbance produced by a third body. — The move- 
ment of two bodies under their mutual attraction 
was completely solved by Newton. When there are 
more than two bodies the problem becomes one of 
great difficulty. In the solar system the mass of the Sun 
is so preponderating that the movement of each planet 



54 ASTRONOMY 

is very largely determined by the Sun. However, 
other planets influence the movement to some extent, 
and " perturb" the motion in an ellipse round the 
Sun as focus. Newton pointed out some of the effects, 
but in the main left this question to his successors. 
The Moon's motion is particularly difficult because, 
although the Sun is very distant compared with the 
Earth, its great mass makes its effect considerable. 
Newton showed how the rotation of the apse and the 
node discovered by Hipparchus were traceable to the 
Sun's action. 

The "Principia." — Newton's discoveries, though many 
of them were made earlier, were published in the 
Principia in 1687. The doctrine of universal gravita- 
tion did not commend itself to the most eminent of 
Newton's scientific contemporaries. In 1738 Voltaire 
presented a popular account of it which procured its 
acceptance among French scientists. From that time 
till the early years of the nineteenth century the idea 
of universal gravitation was developed by great 
French mathematicians, who applied it in detail to 
all the movements of the solar system. 

The task was one of extreme difficulty. The law 
of gravitation, which gives the forces that different 
bodies exert on one another, enables the rate at which 
the velocity of any body is changing to be calculated. 
When this is done, if the velocities are known at one 
particular instant, they may be found a minute later. 
In this minute the positions of the bodies have all 



THE LAW OF GRAVITATION 55 

changed, the forces between them consequently 
altered, and the velocities are changing at slightly 
different rates. The difficulty consists in devising 
mathematical methods for duly integrating the effects 
of these varying forces. The greatest mathematicians 
have applied themselves to various branches of the 
subject, and gravitational astronomy has been a great 
stimulus to mathematics. 

Stability of Solar System. — The work is of too tech- 
nical a character for much of it to be referred to here. 
One important result may be mentioned. Laplace, 
the greatest exponent of gravitational astronomy 
since Newton, demonstrated the stability of the 
solar system. If the Earth were the only planet, it 
would perpetually repeat its path in the same ellipse. 
One effect of the attraction of the planets on each 
other is to slowly change each other's orbits. For 
example, the ellipse in which the Earth moves is at 
present gradually becoming more circular from this 
cause, and the plane of its motion — the ecliptic — 
is slowly changing. Laplace showed that the mean 
distance of each planet from the Sun remains un- 
changed, and that the eccentricities and inclinations 
of their orbits only suffer periodic changes, and these 
between comparatively narrow limits. Thus the 
action of the planets can never make the Earth's 
ellipse so eccentric that the Earth will at one part of 
its orbit approach very near to the Sun, and at the 
opposite part go to a correspondingly great distance 



56 ASTRONOMY 

from it. Laplace showed that this result depends on 
the fact that the Earth and planets are all moving 
round the Sun in the same direction. 

Discovery of Neptune. — In the year 1846, 160 years 
after the publication of the Principia, the law of 
gravitation led to the discovery of a new planet. 
Uranus, a planet beyond Saturn discovered by Her- 
schel in 1781, did not conform exactly to its elliptic 
orbit. The perturbations caused by Jupiter and Saturn 
did not account for the anomalies in its movement. 
The possibility of an exterior planet being the cause 
was investigated simultaneously by Adams at Cam- 
bridge and Leverrier at Paris. From the researches of 
these two astronomers, the position in the sky where the 
disturbing body was to be found was pointed out. 
Search was made by Dr. Galle at Berlin, and the new 
planet (to which the name of Neptune was given) was 
duly found close to the predicted place. 

Halley's Comet. — Another interesting episode con- 
nected with the law of gravitation is furnished by the 
history of Halley's comet. Halley made observations 
of a comet which appeared in 1682, and deter- 
mined the position of its orbit. He found that the 
comet had moved in much the same path as the 
comets which appeared in 1531 and 1607. He con- 
cluded that these were the same comet; that this 
comet moves round the Sun in a very elliptic orbit, 
going to a distance of 33 times the Earth's distance 
from the Sun; and that the comet takes about 75 



THE LAW OF GRAVITATION 



57 



years to complete its revolution, the time varying 
somewhat in consequence of perturbations caused by 
planets near which it passes. The comet is only 
visible at its successive returns to the Sun when it is 




Diag. XXIX. 

comparatively near the Earth. Halley predicted its 
return for the year 1759. Before the reappearance of 
the comet, Clairaut, calculating the perturbing effects 
of the planets it had encountered in its path, pre- 
dicted that the comet would be at the point of its 
orbit nearest to the Sun or at perihelion on April 13, 
1759. The comet was discovered at the end of 1758, 
and Clairaut's prediction found to be only one month 
in error. It again returned to perihelion on Nov. 15, 
1835, and its coming return in April 1910 was pre- 
dicted by Messrs. Cowell and Crommelin of the 




58 ASTRONOMY 

Greenwich Observatory with an error of only three 
days. The early history of this comet is interesting, 
as it has been identified with comets of which historic 
records are preserved. Diagram XXX, taken from the 
Bayeux tapestry, represents a comet which appeared 
in 1066, and was accounted an evil omen for King 
Harold. Calculation shows that Halley's comet in that 
year made one of its periodical visits to the Sun, and 
was unquestionably the one which was supposed to 

have predicted Harold's de- 
feat and death. The comet's 
course has been traced back 
by Messrs. Cowell and 
Crommelin, and is almost 
Diag. XXX. certainly the one which 

Chinese records state to have been seen in 87 B.C., 
and possibly a still earlier one in 240 B.C. 

Movement of the Moon. — The determination of the 
Moon's movements from the law of gravitation has 
been a mathematical problem of great difficulty and 
complexity. The problem has a practical bearing, 
for if the Moon's position can be predicted with 
sufficient accuracy, it may be used to determine longi- 
tude at sea. In 17 13 a prize of ,£20,000 was offered 
by the British Government for a method of finding 
longitude accurate to within half a degree. This prize 
stimulated the manufacture of chronometers on the 
one hand, and the formation of accurate lunar tables 
on the other. In 1765 ^3000 was paid to the widow 



THE LAW OF GRAVITATION 59 

of Tobias Mayer for his tables of the Moon — tables 
which gave the position of the Moon with an accuracy 
of about one minute of arc (^th) of the Moon's 
angular diameter. 

Theories of the Moon were developed with great 
mathematical skill by Clairaut, Euler, and Laplace, 
and various difficulties were removed, but a theory 
which will give the position of the Moon's place as 
accurately as it can be observed is required before 
the law of gravitation can be said to be completely 
verified. Elaborate theories of the Moon's motion 
have been worked out by many eminent mathe- 
maticians. At present Hansen's is used by the 
Nautical Almanac for the prediction of the Moon's 
place, and gives the position of the Moon for the 
period 1750 — 1850 with errors not larger than 1" or 2" 
(i ;/ is about yg^othpart of the Moon's diameter). As 
showing how complicated this question is, it may be 
enough to say that the final algebraic expressions 
which give the position of the Moon in Delaunay's 
Theory occupy a large quarto volume. Not only 
does the Sun affect the motion of the Moon round the 
Earth, but the planets, too, have their influence, both 
directly by their attraction on the Moon, and in- 
directly by their attraction on the Earth. The interest 
of the problem does not consist entirely in surmount- 
ing the mathematical difficulties but in determining 
whether, when all its consequences are traced, the 
simple law of gravitation is a complete key to these 



60 ASTRONOMY 

very complicated movements. Compared with what 
has been already explained, what yet remains in doubt 
is trivial. Still, there are several curious differences 
between observation and gravitational theory in the 
motion of the Moon, and also of Mercury and Venus, 
of which the explanation seems at present to be a 
long way off. 

Mass of Earth. — We have seen how the masses of 
the heavenly bodies can be compared with one 
another, the Sun with the Earth or Jupiter with the 
Earth, by comparing the movements their attractions 
produce upon bodies subject to their influence. But 
what is the mass of the Earth ? This can be measured 
in several ways by comparing its attraction with that 
of a smaller body whose mass is known. 

Attraction of Schehallien. — In 1776 Maskelyne com- 
pared the attraction of the Earth with that of the 
mountain Schehallien in Perthshire. As shown in 
Diagram XXXI, the effect of the attraction of this 
peak is to deflect the plumb-line towards it. The 
amount of this deflection is measured astronomic- 
ally by observing the angle which the direction of 
a star makes with the plumb-line at two stations on 
opposite sides of the mountain. If there were no 
mountain, the angle between the plumb-lines at 
the two places would be the angle AOB, got by 
joining the places to the centre of the Earth. By 
measuring the distance AB this angle can be calcu- 
lated. But owing to the attraction of the mountain 



THE LAW OF GRAVITATION 



61 




which pulls the plumb-line in different directions at 

A and B, the actual 

measured angle is found 

to be greater than the 

angle AOB. The amount 

of the excess is due to the 

pull of the mountain, 

which is thus compared 

with the pull of the Earth. 

In this way Maskelyne 

found the attraction of the 

Earth to be 4.7 times as 

large as it would be if the 

Earth were of the density 

of water throughout; or the Earth's mean density is 

47 times that of water. 

Cavendish. Experiment. — A better and more accurate 
determination is obtained by measuring in a labora- 
tory the attraction of a metallic ball on a small ball 
placed near it. This experiment was first made by 
Cavendish, and was carried out later with great skill 
by Francis Baily by means of a torsion balance. A 
light arm, at the ends of which are two gold balls, 
is suspended by a thread. Suppose the balls rest in 
a position due north and south. If two large balls 
are brought near them, on the east side of one and 
west of the other, the two gold balls will be attracted 
slightly, and the force of the attraction is measured 
by the twist given to the thread. This experiment 



62 



ASTRONOMY 



was carried out by Prof. Boys in 1893 in the cellar 
of the Clarendon Physical Laboratory at Oxford with 
the greatest precision. Observations were made on 
Sunday nights between midnight and 6 a.m., because 
at other times traffic over stony streets and shunting 





HI 


"^ 




% 






% 




1 / 


1 




t v 






' 






*4 / 






^~~^\ 




1 


GM 







M 



Diag. XXXII. 

of trains set up tremors which interfered with the 
delicacy of the experiment. A fine quartz fibre held 
the balls, which were of gold, and in different experi- 
ments were ^th and ^th of an inch diameter. The 
large balls were of lead, and in different experiments 
varied from 2\ to 4J inches in diameter. These ex- 
periments showed that the Earth's mean density is 
5*5270 times that of water. 



CHAPTER IV 



ASTRONOMICAL INSTRUMENTS 

The stars appear to us as bright points fixed on a 
distant globe which turns uniformly. The first task 
of practical astronomy is to map their positions on 
this globe as accurately as possible. Instruments 
have gradually been evolved by which this mapping 
is carried out with ever-increasing precision. 

Right Ascension and Declination. — It is first necessary 
to see clearly how positions on the celestial sphere are 
defined. Suppose P to 
be the pole, and that 
there is a star at S. The 
distance of the star from 
the pole is measured by 
the angle POS, or by 
what is the same thing, 
the arc PS of the sphere. 
The plane OPS will pass 
through P 7 , the other pole, 
and will cut the sphere 
in^ a circle. The circle Diag XXXIII 

90 away from P (it is 
also go° away from P ; ) is called the equinoctial or 




64 ASTRONOMY 

sometimes the equator. PS is called the north polar 
distance of the star, and SM the declination. If PS 
is known, SM is obtained by subtracting PS from 90 . 
If S is north of the equator the declination is positive, 
and if south negative. To know the position of S on 
the sphere, besides knowing SM, we need to know the 
position of M. A point on the equator called the First 
Point of Aries (T), which moves with the stars, is used 
as the point from which to measure, and the arc TM 
(or the angle between the planes POT and POM) 
is called the right ascension. The direction TM is 
measured in the direction contrary to that in which 
the Earth rotates, and may have any value from o° 
to 360 . The point T is not chosen arbitrarily, but is 
the point in the sky where the ecliptic or path of the 
Sun cuts the equator. It will be seen that this mode 
of defining the position of a star in the sky is similar 
to the method of defining a spot on the earth by its 
latitude and longitude. 

Now 7 as the whole sky appears to turn about its 
axis in one sidereal day (approximately 4 m. shorter 
than the mean solar day which is used in ordinary 
life), the star moves in a circle completing its round 
in one sidereal day. At the moment when it is at 5 
in the diagram, it is on a circle which passes through 
the poles and the zenith, or point vertically over the 
observer's head. This circle is the intersection of the 
celestial sphere with the meridian, or vertical plane 
which passes through the place of observation in a 



ASTRONOMICAL INSTRUMENTS 65 

direction exactly north and south. When S reaches s, 
its right ascension circle PSMP 7 is PsraP 7 , or the 
point M has reached ra. After a time another star 
S 7 reaches the meridian at s 7 , and M 7 reaches ra 7 , and, 
if the interval of time between the meridian-passage of 
S and S 7 be measured, we shall obtain the angle of 
MM 7 at the rate of 15 to one sidereal hour. 

Clocks. — Suppose, now, we have a clock which reads 
oh. o m. os. when T is on the meridian, and is rated 
so that it completes 24 b. when T returns to the 
meridian the next day. The time indicated by this 
clock when any star crosses the meridian gives the 
star's right ascension, at the rate of 360 to 24 hours, 
or 1 5 to 1 hour. It is frequently not necessary to 
change from time to angle, and the right ascension is 
taken as the actual time given by the clock (supposed 
to be correct). Thus it is very necessary for an ob- 
servatory to possess such a clock, to divide up the time 
in which the Earth makes one rotation into 24 hours, 
24x60 minutes and 24x60x60 seconds. The time 
indicated by such a clock gives the right ascensions of 
all stars which are at that moment on the meridian. 

Circles. — When a star is on the meridian its distance 
from the pole is the sum of its distance from the 
zenith and the distance of the zenith from the pole. 
In Diagram XXXIII sP = sZ + ZP. Now ZP is the 
same for all stars, and is obtained by subtracting the 
latitude of the place of observation from 90 . The 
direction of Z is the direction of a plumb line, so that 



66 



ASTRONOMY 



to find sZ it is necessary to observe the angle between 
the direction of the star and the direction of a plumb 
line. The method adopted by Tycho Brahe, though 
not invented, yet brought to a much higher degree of 





Diag. xxxiv. 



Diag. XXXV. 



accuracy by him, consisted in having a large quadrant 
of a circle mounted on a wall which pointed accurately 
north and south (Diagram XXXIV). The arc of the 
quadrant was divided into degrees and further sub- 
divided into minutes (as in Diagram XXXV). The 
direction of the star was taken along sights, one of 
which was at the centre of the quadrant and the other 
moved to the required position along the arc for the 
star to be seen. In this way Tycho Brahe observed 
the positions of stars and planets with errors of not 
more than i 1 or 2 f . 

The accurate graduation of the arc of a circle is an 
art which has been developed with the progress of 
astronomy. Quadrants fixed to a wall are no longer 
used, but complete circles attached to a telescope. 



ASTRONOMICAL INSTRUMENTS 6 7 

An accurately divided circle is as essential for the 
determination of declinations as a good clock is for 
that of right ascensions. The introduction of tele- 
scopes has not altered the method of determining the 
positions of stars. The right ascension of a star is 
still determined by observing the time at which it 
crosses the meridian, and the north polar distance 
from its altitude at this moment. 

The Telescope. — The telescope has increased the 
accuracy and improved the power of the astronomical 
observer in a wonderful manner. It has three import- 
ant properties — 

(i) It increases the amount of light which enters 
the eye from a star, and thus enables fainter stars to 
be seen. 

(2) It magnifies the apparent angle between two 
stars, and thus greater accuracy can be obtained in 
angular measurements. 

(3) It obviates the necessity for the use of sights. 
The light from a star comes to us in parallel rays. 

If these fall on a lens (Diagram XXXVI) their direc- 



Tefy* 



Diag. XXXVI. 
tions are refracted so that they pass through a point F, 

F 2 




68 ASTRONOMY 

the focus of the lens. At F a bright point is formed, 
called the image of the star. If the rays which pass 
through F be intercepted by a second lens L', they can 
be again converted into a parallel beam of light. If 
the diameter of the second beam is no wider than the 
pupil of the eye, all the star's light which fell on the 
lens L passes into the eye. The telescope, in effect, 
supplies the astronomer with an eye as big as its 
object glass and thus enables him to see very much 
fainter stars. 

Now let there be two stars whose images are formed 
at F and G (Diagram XXXVII). The cone of light 




Diag. XXXVII. 

through F will be converted into a beam of parallel 
rays which, falling on the eye, will enable the star to 
be seen. Similarly the cone of rays through G will 
be converted into a parallel beam. The first beam is 
in a direction parallel to DF, and the second one 
parallel to DG. Thus the eye which receives these 
beams will see the two stars in directions parallel to 
DF and DG, whereas the actual directions are CF 
and CG. Thus the angular distance between the stars 
is magnified from FCG to FDG, which is in the pro- 
portion CE : DE, or that of the focal length of the 



ASTRONOMICAL INSTRUMENTS 69 

object lens to the focal length of the eye lens. Thus 
the longer the focal length of the object glass of a 
telescope and the shorter the focal length of the eye- 
piece, the greater the magnification. 

Suppose the two lenses are firmly fixed in a tube, 
and in the focal plane FEG two pieces of fine wire or 
two spider's webs are stretched, crossing at E. When 
the telescope is pointed near a star an image is formed 
in the plane FEG. Shifting the telescope a little the 
image can be made to fall at E, the intersection of the 
two fine spider's webs. In this case the telescope is 
pointing accurately to the star, for the line EC then 
passes through the star. As E is fixed and C is 
fixed, the line EC serves the same purpose as sights 
at E and C ; and it is much easier to secure accurate 
pointing in this way. This important improve- 
ment of the telescope was introduced by Gascoigne in 
1640. 

Refracting Telescope. — Telescopes have been gradually 
improved from the small and imperfect one of Gali- 
leo's to the large refractors and reflectors of the present 
day. A simple lens does not bring light of all colours 
to the same focus, and the image formed is con- 
sequently coloured and indistinct. Newton, who first 
resolved white light into a coloured band by means of 
a prism, supposed that this defect was irremediable. 
But in 1758 Dollond, an English optician, found that 
by combining a convex lens of crown glass (a dense 
glass with large refracting power) with a concave lens 
of flint glass (a lighter glass of less refractive power), 




7 o ASTRONOMY 

the defect can be largely remedied. The light from a 
star falling on the crown lens is refracted into a con- 
verging beam, and is also dispersed into the different 
colours of the spectrum : the 
concave lens of flint glass neutral- 
izes the dispersion and makes the 
Din xxxvin ■ ra y s °f different colours converge 
to the same point. This combina- 
tion of lenses is called an achromatic object glass 
(Diagram XXXVIII). It is not possible to com- 
pletely banish all trace of colour in this way, and 
there are other imperfections arising from the fact 
that the curvature of the surfaces does not bring all 
parallel rays of the same colour absolutely to a point. 
These " aberrations/' chromatic and spherical, are 
reduced to small dimensions by careful choice of the 
kinds of glass and by calculating the most appropriate 
curvatures for the surfaces of the two lenses. The 
single lens at the eye-end of a telescope has also been 
replaced by two separated from one another by a 
distance in suitable relation to the curvatures of the 
two lenses. In this way an increase in clearness is 
obtained in the parts of the image which are near the 
edge of the eye-piece. 

Before the invention of the achromatic object glass 
very long telescopes were used, because they gave 
greater magnification without much indistinctness 
from the confusion of colours. With an achromatic 
object glass much more magnification of the image 



ASTRONOMICAL INSTRUMENTS 71 

by the eye-piece is possible, and telescopes are not so 
cumbersome. 

For a long time it was not possible to procure glass 
discs of sufficient uniformity and clearness to make 
object glasses of more than 3 inches in diameter. The 
largest object glass constructed by Dollond had a 
diameter of 3§ inches. Early in the nineteenth cen- 
tury a Swiss artist, Guinand, succeeded in making 
larger discs. He was employed by Fraunhofer, who 
constructed object glasses of great perfection of 6 to 9 
inches aperture. In 1840 a 15-inch object glass was 
constructed by Merz for the Imperial Observatory at 
Pulkowa; in 1870 a refractor of 25-inches aperture 
was made by Messrs. Cooke for Mr. R. S. Newall, 
and there are at the present time a considerable number 
of telescopes whose object glasses are as large or larger 
than this. The largest refracting telescopes are those 
of the Lick Observatory of 36-inches aperture, and of 
tlie Yerkes Observatory of 40-inches aperture, both 
made by the American opticians, Alvan Clark & Sons. 

Reflecting Telescope. — In 1668 Newton made a small 
reflecting telescope which magnified thirty times. In 
this instrument the light from a star falls on a concave 
mirror of speculum metal — an alloy of copper and 
tin approximately in the proportions of four atoms of 
copper to one of tin. The light is reflected by the 
mirror so that parallel rays from a star are brought 
to a focus forming an image of the star. By the 
insertion of a small flat mirror, placed diagonally in 




Diag. XXXIX. 



72 ASTRONOMY 

the tube, this image is shifted to the side of the tele- 
scope, where it can be viewed by an eye-piece (Dia- 
gram XXX IX). In 
1723 Hadley, the in- 
ventor of the sextant, 
made a reflector with a 
mirror of 5J inches and 
a focal length of 62 
inches with which a magnification of 200 times could 
be obtained. The great development of reflecting 
telescopes was made from 1 776-1 7S7 by Sir W. 
Herschel, who constructed specula of 6, 8, 12, 18, 24 
and 48 inches, with focal lengths of 7, 10, 14, 20, 25 
and 40 feet. These great telescopes were exceeded 
by Lord Rosse who, in 1848, constructed a reflecting 
telescope of 6 feet diameter and 53 feet focal length. 

In 1 85 1 Liebig discovered a process of depositing 
silver on glass so as to give a highly reflecting surface. 
Since that time reflecting telescopes have usually been 
made of glass with a fine film of silver deposited on 
them chemically. The advantages are a more highly 
reflective surface, less weight, and the facility with 
which a tarnished silver film may be dissolved and a 
fresh one deposited without in any way interfering 
with the carefully figured surface of the glass. 

Astronomy is greatly indebted to Dr. Common, an 
English amateur astronomer, for introducing the use 
of large silver-on-glass reflectors. With a 36-inch 
mirror he obtained in 1883 a beautiful photograph of 



ASTRONOMICAL INSTRUMENTS 73 

the Orion nebula. He completed in 1890 a mirror of 
5 feet diameter, and showed how to grind, polish and 
test a mirror so as to obtain the best results. The 
greatest living exponent of the art of making very 
large mirrors is Mr. Ritchey, who has constructed 
extremely perfect ones for the Yerkes and Mt. Wilson 
Observatories in America. He has recently constructed 
one of 60 inches diameter, and is now engaged on one 
of 100 inches. 

There has been throughout the long period of their 
development a friendly rivalry between the refracting 
and reflecting telescopes. The uses of the two instru- 
ments are now pretty well defined. Where accurate 
measurements are required the refractor is generally 
to be preferred. Where the object observed is ex- 
tremely faint the reflector has the advantage, for in 
proportion to size reflecting telescopes are of much 
shorter focal length, thus producing a smaller but 
brighter picture. 

Mounting of Telescopes. — A small telescope, which is 
used simply to look at the stars, can be held in the 
hands, but it will be found much easier to rest it on 
something, and for one of moderate dimensions 
some form of mounting which holds the telescope 
firmly and yet admits of its being easily pointed to any 
part of the sky is indispensable. When accurate 
measurements of any kind are to be made, the mount- 
ing is a matter of great importance. There are two 
classes of observations for which the telescope is used, 



74 ASTRONOMY 

which require it to be mounted in entirely different 
ways. The actual position of the heavenly bodies in 
the sky may be required, as for instance in finding 
day by day the positions of the Sun, Moon or planets, 
or determining the positions of the stars. On the 
other hand, the position of the object in the sky may 
be of no interest, as in observations of the revolution 
of Jupiter's satellites about the planet or the rotation 
of Jupiter itself. 

When the actual position of a star in the sky is to 
be determined, the telescope is fixed during the time 
of observation, and the star is w 7 atched as it moves in 
front of the telescope. The image of the star is seen 
as a bright point moving in the focal plane of the 
objective; in this focal plane spider's webs are 
stretched, and the observation consists in a determina- 
tion of the exact position of the telescope, and the 
exact time at which certain threads are crossed by the 
star's image. 

Transit - Circle. — The most important instrument of 
this kind is the transit-circle (Diagram XL). It 
applies the advantages the telescope gives in visibility, 
magnification and accuracy of sighting to the method 
used by Tycho Brahe of observing the time when a 
star crosses the meridian and its altitude at that 
moment. The telescope is fixed perpendicularly to 
a horizontal axis which ends in two accurately turned 
pivots. These pivots rest in bearings due east and 
west, so that the telescope can be turned to any point 



ASTRONOMICAL INSTRUMENTS 



/a 




| 



7 6 



ASTRONOMY 



in the meridian (or vertical plane pointing north and 
south), but is always confined to this plane. In the 
focal plane of the objective are two fairly close 
horizontal parallel wires and several equally distant 
perpendicular ones (so-called wires, but in reality 
spider's webs) (Diagram XLI). The middle wire is 
so placed that it is the "sight" of the meridian, i. e. 
when a star crosses the meridian its image will be 
seen in the telescope crossing the middle wire. A 
little before the time when a star should cross the 
meridian the observer turns the telescope about its 
axis to the right altitude. In due time he sees the 
star enter the field of his telescope, and moves the tele- 
scope so that the star may come accurately in the 
middle of the two horizontal wires. The star is 
watched as it moves and the exact time is noted when 
the several vertical wires are crossed. Formerly the 
timing was done by the observer listening to the beats 

of a clock, carrying the 
seconds in his head and 
estimating the tenths of 
seconds. An easier method 
now in general use is to 
register the time electrically 
on a chronograph, the ob- 
server pressing a button 
when the star crosses the 
wires. The mean of the 

Diag. XLI. 

times across these wires 
gives, subject to some small corrections which are 




ASTRONOMICAL INSTRUMENTS 77 

easily calculated, the exact moment at which the star 
crosses the meridian, i. e. the right ascension. 

To obtain the star's declination it is necessary to 
determine the altitude at which the telescope is 
pointed. For this purpose a large graduated circle is 
fixed centrally on the axis of rotation of the telescope ; 
the position of the telescope is determined by the par- 
ticular division on the circle which comes to some 
fixed point. To secure greater accuracy microscopes 
are firmly fixed in positions for viewing the graduated 
limb of the circle. 

In the focal plane of each microscope are placed 
wires, and the intersection of these wires will be seen 
between two divisions of the graduated circle. The 
exact distance of this point from a division is obtained 
by mounting the wires on a frame carried by a screw 
and reading the turns and fractions of a turn of this 
screw necessary to bring the cross to the nearest 
division of the circle. The divisions of circles are 
generally 5' apart (so that there are 12x360 on the 
whole circle), the fractions of 5' being read by means 
of the micrometer screw. For greater accuracy four 
or six microscopes arranged round a circle are used. 

In actual practice there are a number of modifica- 
tions and complications. With a good instrument, a 
good clock and good observer, the right ascension 
and declination of a star can be determined with an 
error which is seldom more than 2" . To form an idea 
of 2" comparison may be made with the angular dia- 
meter of the Sun, which is 30' or 1800". By taking 



78 ASTRONOMY 

the mean of several observations on different nights, 
stars' positions are found with greater accuracy. 

Equatorial. — In order that a telescope may be kept 
pointing to a star as it crosses the sky the telescope 
must be given a suitable movement. The movement 




Diag. XLII. 



required is easily demonstrated by a pair of compasses. 
If one leg be pointed towards the pole, the other leg 



ASTRONOMICAL INSTRUMENTS 79 

can be opened out to an angle equal to the polar 
distance of the star; then by turning about the leg 
pointing to the pole the other leg may be brought to a 
position in which it points to the star. If now the 
compasses are turned uniformly around the leg point- 
ing the pole so as to go completely round in one 
sidereal day, the other leg will point to the star all the 
time. This is exactly the principle of the equatorial 
mounting of a telescope. The telescope is perpen- 
dicular to, and can turn about, the declination axis. 
The declination axis is perpendicular to, and turns 
about, the polar axis (Diagram (XLII). The tele- 
scope is first placed in the required position and then 
turned by clockwork. 

In the mounting of a large telescope there are neces- 
sarily many important details to be arranged in order 
to make it easy of manipulation and regular in its 
movement. It is also necessary to be able to correct 
for any want of precision in the driving clock, espe- 
cially when the telescope must be kept pointing to 
the same part of the sky for a long time. These 
details are satisfactorily surmounted by the engineer- 
ing skill of the instrument makers combined with care 
and patience of the astronomer who uses the equatorial. 

Thus a picture of the part of the sky to which the 
telescope is pointed is formed in the focal plane of the 
object glass. By means of the equatorial movement 
this picture is kept at rest, and the observer looking 
through the eye-piece of the telescope can examine it. 



So 



ASTRONOMY 



Position-Micrometer. — This examination usually in- 
volves measurement of some kind, and other instru- 
ments are required for this purpose. For example, 
to measure the distance between two very near stars 
or the diameter of one of the planets, a micrometer of 
some kind is needed. A very simple form is the posi- 
tion-micrometer, which gives means of moving fine 
wires (webs of spiders stretched on frames) in the focal 




Diag. XLIII. 

plane of the telescope. In Diagram XLIII, which 
represents this instrument, there are three lines, AB, 
CC and DD, of which CC and DD can be moved 
nearer or farther apart by means of screws P and Q, 
the distance between them being known from the 
readings of the screw-heads. In addition the micro- 
meter, which is mounted in the telescope tube, can be 
turned to any required position. Thus if two stars 



ASTRONOMICAL INSTRUMENTS 81 

are in the field of view, by turning the micrometer and 
moving the screws, the intersection of AB and CC 
can be placed on one star and the intersection of AB 
and DD on the other. 

The distance between the images of the two stars is 
measured in linear measure, let us say, in fractions of 
an inch ; the angle between them is found by dividing 
this distance by the focal length of the telescope. 
Referring to Diagram XXXVII, the distance FG 
is measured, and to find the angle FCG it is sufficient 
to divide by the length CE, as we are only dealing 
with very small angles. 

Heliometer. — A position-micrometer is suitable for 
measuring the distance between two stars which are so 
near that both can be seen at the same time. With a 
large telescope this means angles less than one minute 
of arc — or less than ^th of the diameter of the Sun or 
Moon. For angles comparable in size with the Sun's 
diameter the most accurate visual observations are 
made with a heliometer. This is a telescope equatori- 
ally mounted, but having its object glass divided into 
two halves. The two halves can be moved, as shown 
in Diagram XLIV, by means which admit of the 
distance from the central position being accurately 
determined. Each half gives a picture of the part 
of the sky which is being observed; the two images 
are exactly alike, but they are at a distance apart 
equal to the separation of the two halves of the 
object glass. If, for example, two stars are looked at, 

G 




82 ASTRONOMY 

and the glass is turned so that the direction in which 
the halves are separated is parallel to the line joining 
the stars, there will be seen, as in Diagram XLI V, four 

images in a straight line, 
viz. A and B, the images of 
the two stars formed by 
one half of the glass, and 
A ; B 7 , the images formed by 
the other half. The halves 
of the glass are separated by 
V _ Q | a distance AA' or BB ; . If 

Dia xliv now ^ey are St ^ farther 

separated till A' coincides 
exactly with B, the distance between the stars is 
exactly equal to the amount by which the two halves 
of the glass are separated. In practice a good 
deal of refinement is necessary in carrying out these 
observations, and it is, besides, a very delicate matter 
to cut an object glass in two. To instruments of this 
class we are largely indebted for the accurate measures 
by which the distances of the Sun and of the stars 
have been determined. 

Photographic Telescope. — The telescope is seen in its 
simplest form when it is used for photography. A 
photographic plate is placed in the focal plane of the 
object glass or reflector, and gives a permanent record 
of the image formed there. 

A reflector may be used for visual or photographic 
observations because the light of all colours is brought 
to the same focus, but an object glass to be used for 



ASTRONOMICAL INSTRUMENTS S3 

photography must be constructed so that blue light 
which affects the plates most powerfully is brought to 
a sharp focus, and not the red, green and yellow to 
which the eye is most sensitive. A photographic 
telescope is merely a large photographic lens of corre- 
spondingly long focus. Typical telescopes are those 
used in the International Chart of the Heavens, 
initiated at Paris in 1887, of about 13 inches diameter 
and 11 feet 3 inches focal length. The scale of these 
telescopes is such that the photographs of the Sun or 
Moon are about i\ inches in diameter. The field 
over which good pictures are taken has a diameter 
of about 5 inches. Using fast plates, stars visible to 
the naked eye require exposures of less than one 
second, and the number of stars shown increases 
largely with the length of the exposure. Long 
exposures are necessary to photograph very faint 
stars, and therefore the clock movement should be 
very accurate. If the telescope moves to follow the 
motion of the stars exactly their images will be round 
dots, but if it is moving too slowly or too fast they will 
be short lines. To secure the correct movement of the 
telescope arrangements are made for the observer to 
guide and control it. 

When a photograph of the stars has been taken, 
it will contain a small number of bright stars whose 
positions are already known and a large number of 
fainter ones which are unknown. It therefore serves 
to fill in the fainter stars into a map on which the 
brighter stars are already delineated. Like the helio- 

G 2 



84 ASTRONOMY 

meter, a photograph can be used for finding the 
distances and relative directions of stars whose 
distance apart is less than one or two degrees. 

We have so far considered astronomical instru- 
ments simply as means for the accurate measure of 
angles — the transit circle being typical of the methods 
by which the relative positions of stars distant from 
one another on the celestial sphere are obtained, and 
the equatorial mounting with its various adjuncts 
giving the relative positions of near bodies. But a 
telescope mounted equatorially can be used for many 
other purposes. For example, a photometer may be 
used, and the quantity of light received from different 
stars may be measured and compared. In one or 
two cases an instrument has been attached to the 
telescope by which the amount of heat received from 
the stars has been measured. But by far the most 
important instrument of physical research used by 
the astronomer in conjunction with the telescope is 
the spectroscope. When applied to the stars it is 
mounted on an equatorial telescope with the slit in the 
focal plane of the object glass. The telescope is so 
pointed that the image of a star may fall on the slit 
and part of it enter the spectroscope. The function 
of the object glass is to collect the light, and that of 
the equatorial to keep the telescope accurately pointed. 
The way in which a spectroscope analyzes the light 
which passes through it will be described in the chapter 
on the Sun. 



CHAPTER V 

THE SUN'S DISTANCE 

The determination of the Sun's distance is one of 
the most important problems of astronomy. As we 
have seen, it is possible, by means of Kepler's third 
law, to determine the distances of the other planets 
from the Sun in terms of the Earth's mean distance. 
For example, the mean distance of Jupiter from the 
Sun is 5'2028 times the Earth's distance. A model 
of the solar system can be constructed, but till the 
Earth's distance from the Sun is found we cannot 
give the scale. More than this, the distances of the 
stars are determined in terms of the distance of the 
Sun, so that this is the standard length with which 
all astronomical distances are compared. Naturally 
such an important problem has received a great deal 
of attention. 

A Greek astronomer, Aristarchus of Lamos, realiz- 
ing that the Moon shone by reflected light from the 
Sun, argued that the Moon would be exactly half full 
when the directions of Sun and Earth, as seen from the 
Moon, were at right angles. Thus in Diagram XLV 

85 



86 ASTRONOMY 

the angle EMS is exactly a right angle. If the exact 
moment when the Moon is half full could be deter- 
mined by observation, it would then be possible, by 
measuring the angle between the Sun and Moon, as 

seen from the Earth 
^ ~^"" ; (the angle SEM of the 




diagram), to determine 
Diag. xlv. ^he exact shape of the 

triangle SME, and 
thus find SM in terms of EM. He found in this way 
that the Sun's distance was nineteen times that of the 
Moon. The method is extremely rough, because it is 
impossible to say exactly when the Moon is half full. 

Till the time of Kepler this was the generally 
accepted distance of the Sun, but Kepler showed that 
it must be at least three times as far away. 

Cassini's Measure of Sun's Distance. — The first deter- 
mination which approaches to what we now know to 
be the distance w 7 as made by the French astronomer 
Cassini, between 1670 and 1680. He did not measure 
the distance of the Sun directly, but chose the planet 
Mars when in opposition, i. e. in a direction opposite 
to the Sun. Now, the Earth describes a circle of 
radius 1 about the Sun, while Mars describes one of 
radius ij, and therefore Mars, when in opposition, as 
at M (Diagram XLVI), is only at one-half the Sun's 
distance. The shorter distance is measured twice as 
easily. But more than this, Mars is seen at night with 
a background of stars, and its position can be deter- 



THE SUN'S DISTANCE 



87 



mined very accurately in relation to these stars. 
Cassini sent out an expedition to Cayenne, and the 
positions of Mars were observed simultaneously from 
Paris and Cayenne. In Diagram XLVII, E is the 
centre of the Earth, EP^ a radius through Paris, and 
ECc one through Cayenne, while M is the position of 
Mars. Tf at Paris the angle MPp is measured, and 




Dia£. XLVI. 



Diag. XLVII. 



simultaneously at Cayenne the angle MCc, then, since 
the radii of the Earth, EC and EP, are known, and 
also the angle PEC from the positions of Paris 
and Cayenne on the Earth's surface, there is enough 
determined to draw the diagram accurately to scale, 
and thus find the distance EM. In actual practice the 
diagram would not be drawn to scale, but trigono- 
metrical calculations made instead, but this is merely 
a substitute which avoids the difficulties and uncer- 
tainties of drawing the angles correctly. 

Cassini's result was 84 million miles, and as we now 
know th'e distance to be 93 million miles, it will be 



8S ASTRONOMY 

seen that he was within about 10 per cent, of the true 
value. 

Transit of Venus. — Another and very famous 
method of determining the Sun's distance is by the 
transit of Venus. As the orbit of Venus lies within 
that of the Earth, it happens on very rare occasions 
that Venus passes between the Earth and the Sun, 
and is actually seen crossing the Sun's disc as a black 
spot. As at these times Venus is about 25 million 
miles from the Earth, while the Sun is much farther 
away, it follows that, seen from two points as distant 




Diag. XLVIII. 

from one another as possible on the Earth's surface, 
Venus traces a slightly different path across the Sun's 
disc. This is shown in Diagram XLVIII, but im- 
mensely exaggerated. By observations of the exact 
times at which Venus enters and leaves the Sun's disc 
at the two stations, it is possible to determine the dis- 
tance apart in angle of the two chords aa! and bb 1 
and thence to find the distance of Venus — the distance 
AB Between the two stations serving as the base-line. 
Observations made at the transits of 1761 and 1769 
gave the distance of the Sun 95 million miles. An 



THE SUN'S DISTANCE 



89 



attempt was made at the transits of 1874 and 1882 to 
obtain the distance with greater accuracy. Extensive 
preparations were made, and many expeditions were 
dispatched by the governments of Europe and the 
United States. Although every care was taken, the 
expeditions were a comparative failure, owing to the 
impossibility of saying with certainty what was the 
exact moment at which Venus was seen touching the 
Sun's disc. 

Mars near Opposition. — In the year 1877 Sir David 
Gill made observations of Mars near opposition from 
the island of Ascension. As the Earth turns round, 
bringing the observer 
from A in the early 
evening to B in the 
early morning (Dia- 
gram XLIX), the di- 
rection in which Mars 

is seen changes slightly. Instead of observing Mars 
simultaneously from two different places on the Earth's 
surface, it was observed evening and morning from the 
same point — the point of observation swinging in con- 
sequence of the Earth's rotation from one side to the 
other of the direct line from the Earth's centre to 
Mars. Are there any means of measuring the angle 
AMB ? If so, the distance can be found. Now 
Mars is seen projected on the sky in the midst of the 
fixed stars. These are so distant that they are seen 
in the same direction from all points of the Earth's 




* To Star 



Piacr XLIX. 



9 o ASTRONOMY 

surface. Suppose there were a star exactly in the 
line of EM. As seen from A, Mars would appear 
to the right of this star, but when the Earth's rotation 
will have carried A to B, then it will appear to the 
left. Measuring the angular distances between Mars 
and the star, the angles MAS and MBS are found, 
and by addition the angle AMB. Then, as the length 
AB can be easily determined, the distance EM is 
calculated at once. 

The geometrical principles underlying this are easy 
enough, but observations necessary to obtain a good 
determination of the distance must be of extreme 
accuracy. The angles to be measured are so extremely 
small that the slightest errors make a considerable 
difference in the result. The measures of angles were 
made with a heliometer, and errors arising from the 
instrument and the observer were guarded against, and 
where possible their effects eliminated by further ob- 
servations. An additional difficulty is found in the 
movement of the planet. Mars does not stay still 
between evening and morning to suit the observer's 
convenience, so its motion has to be carefully calcu- 
lated and allowed for. As Mars is near opposition for a 
considerable time, long series of observations are car- 
ried on night after night and morning after morning, 
and the final result derived from the mean of the whole 
series. Although a very accurate result was obtained, 
the fact that Mars has a disc of considerable size gave 
rise to a little uncertainty. It is much easier to 



THE SUN'S DISTANCE 91 

measure the distance of a bright point from another 
than to measure the distance of a bright point from 
the edge of a disc, where one is liable to measure 
from a little inside or a little outside of the edge. 
Now, there are among the small planets whose orbits 
are rather further from the Sun than that of Mars, 
some which, owing to the eccentricity of their orbits, 
come sufficiently near to the Earth for them to be 
available to determine the Sun's distance. From these 
Sir David Gill picked out Victoria, Iris and Sappho 
as being the most suitable, and made an extensive 
series of observations at the Cape of Good Hope in 
the years 1888 and 1889, and also secured the assist- 
ance of observers at northern observatories in the 
observations of the planets, and in the extensive sub- 
sidiary observations necessary to determine the posi- 
tions of the stars from which the angular distances of 
the planets were measured. The details of the ob- 
servations and the determination of the Sun's distance 
from them occupy two large quarto volumes. The 
final result is that the Sun's distance is 92,874,000 
miles, and from the agreement between the different 
observations it is concluded that the error is probably 
not more than 5o,oco miles. This error corresponds 
to an error of one yard in measuring a mile. 

Eros. — On August 13, 1898, Dr. De Witt of Berlin 
discovered a small planet, to which the name Eros was 
subsequently given, which at times comes to within 
14 million miles of the Earth. This small body, only 



92 ASTRONOMY 

28 miles in diameter, is our nearest neighbour among 
the planets, and is admirably suited to determine the 
Sun's distance. At the end of 1900, when Eros came 
to within 30 million miles of the Earth, a very exten- 
sive series of observations was undertaken in co- 
operation by many observatories. The method em- 
ployed was essentially the same as the one just 
described with regard to Victoria, Iris and Sappho ; 
the main difference being that photographs of the 
planet and surrounding stars were taken, and after- 
wards measured, instead of the planet's distances 
from neighbouring stars being measured with the 
heliometer. The photographic telescopes employed 
were of long focus — from njft. to 22jft. — and con- 
sequently the photographs were on a large scale, and 
admitted of the accurate determination of the position 
of Eros among the surrounding stars. The result 
derived by Mr. Hinks of the Cambridge observatory 
from the combined observations of Eros is approxim- 
ately 92,800,000 miles, agreeing very closely with the 
distance found by Sir David Gill. 

It should be noticed that the methods of determin- 
ing the Sun's distance just described, though very 
complicated in the details which must be considered 
when a result of high, accuracy is aimed at, are very 
simple in principle. The distance of the Sun is 
measured just as a surveyor might measure the dis- 
tance of a tree on the opposite bank of a river. The 
difficulty arises from the fact that the astronomer 



THE SUN'S DISTANCE 93 

cannot obtain a base-line larger than the diameter of 
the Earth. This, in comparison with the distance of 
Eros, is very small, and gives a triangle with very 
long sides and a very short base. A small error in 
the determination of the vertical angle makes a large 
error in determining the lengths of the long sides of 
the triangle. 

The distance of the Sun may be determined in an 
entirely different way by observing the time which 
light takes to travel across this distance, and again by 
comparing the velocity of the Earth in its' orbit with 
the velocity of light. 

Velocity of Light. — In the year 1675 the Danish 
astronomer Roemer discovered that light is not trans- 
mitted instantaneously, but moves with a measurable, 
though very great, velocity. He was led to this dis- 
covery by observations of Jupiter's satellites. The 
Sun's light causes Jupiter to cast a shadow, and the 
satellites may be seen entering or emerging from this 
shadow. From numerous observations it became pos- 
sible to construct tables predicting the times of these 
occurrences. Roemer found, however, that when the 
Earth was near to Jupiter the eclipses occurred before 
the predicted times, but after them when the Earth was 
more than its mean distance from Jupiter. He ex- 
plained these differences between the observed and pre- 
dicted times by the difference of time taken by the light 
to travel a longer or shorter distance. Thus in Dia- 
gram L, if E x , E 2 , E 3 , E 4 , be four positions of the 




94 ASTRONOMY 

Earth, S and J the positions of the Sun and Jupiter, 
the distances to be traversed in these four cases are 
EJ, EJ, E 3 J, EJ : and it is clear that the difference 

between the times taken 
to traverse E 3 J and EJ 
* gives twice the time it 
ir takes for light to travel 
from the Sun to the 
— T Earth. The actual time 

Diag. L. 

taken by light to travel 
the mean distance between the Earth and Sun is 
8 m. i8*5 s. 

Aberration. — Fifty years later, Bradley, while at- 
tempting to measure the distance of one of the fixed 
stars, y Draconis, discovered the " aberration of light." 
He found that this star's declination changed in the 
course of the year. From December 1725 to March 
1726 the star moved 20" towards the south; it was 
stationary for a short time, and then moved north- 
wards, reaching by the middle of June the position it 
had at the beginning of December. It continued to 
move northwards, till at the beginning of September 
it was 20" to the north of its position in December 
and June. Again it was stationary for a short time, 
and then moved southwards, till at the beginning 
of December it was in the same position as in the 
previous year. 

Although the movements of the star were exactly 
opposite to Bradley's anticipation, their regularity 



THE SUN'S DISTANCE 



95 



showed that they were not accidental. At first Bradley 
looked for the explanation in a movement of the 
Earth's axis. But by making observations of stars 
in different parts of the sky he found that this could 
not be the cause, and after some other attempts he 
discovered that the velocity of the Earth in its orbit, 
combined with the velocity of propagation of light, 
afforded a complete explanation of the phenomena. 
A very familiar example will help to make this clear. 
If rain is falling vertically a person who is standing 
still holds his umbrella directly over his head, but if 
he is walking fast the rain appears to meet him, and 
he holds his umbrella slightly in front. In a similar 
manner, if the light moves over a distance equal to BA 
(Diagram LI), while the observer moves 
over a distance AC, the light will appear 
to come in a direction DA, instead of 
the direction BA. Let us further sup- 
pose that the gentleman with the 
umbrella walks round a circular track. 
When he is walking northwards his 
umbrella will be pointed a little to the 
north, when eastward a little east, 
when southward a little south — the di- 
rection in which he holds the umbrella 
being constantly changed. Now as the Earth is moving 
round the Sun its direction is constantly changing 
throughout the year. The direction from which the 
light appears to come from a star, L e. the direction 




96 ASTRONOMY 

in which the star is seen, is constantly changing — 
being always inclined slightly from the star's mean 
direction towards the direction in which the Earth at 
the moment is travelling, and in consequence the 
stars are seen to describe small ellipses in the sky 
about their mean positions. The semi-major axes of 
these ellipses are all the same, namely, 20" (approxi- 
mately), this being the angle of a right-angled tri- 
angle of which the longest side is proportional to 
the velocity of light, and the shortest proportional 
to the velocity of the Earth in its motion round the 
Sun. 

Sun's Distance determined from Velocity of Light. — 
Roemer's observations showed that light was pro- 
pagated with a finite velocity, and Bradley's discovery 
of aberration was the first absolute proof that the 
earth revolved round the Sun. But in the middle of 
last century methods of measuring the velocity of 
light on the Earth were devised by Fizeau and Fou- 
cault; the method of Foucault by which the velocity 
of propagation of light is measured in a laboratory 
has been so perfected that Michelson and Newcomb 
have determined it as 186,330 miles a second, with an 
error probably not exceeding 25 miles. Knowing the 
velocity of light, if the time which light takes to travel 
across the Earth's orbit be accurately determined from 
the times of the eclipses of Jupiter's satellites, it is 
but a matter of simple division to find the radius of 
this orbit or the distance of the Sun. The accuracy 



THE SUN'S DISTANCE 97 

attainable by this method is considerable, but not 
nearly equal to that given by the trigonometrical 
methods described above. 

The constant of aberration has been determined with 
very great accuracy by observation. This constant is 
the ratio of the Earth's velocity to that of light. 
Knowing the velocity of light, the velocity of the 
Earth is deduced, and from it the distance through 
which the Earth moves in a year, and then the mean 
distance of the Earth from the Sun. The value thus 
found for the Sun's distance is slightly greater than 
the result given on p. 92. 

Quite recently another method has been employed 
for determining the ratio between the Earth's velocity 
and that of light. As will be explained in the next 
chapter, when the light from a star is analyzed by a 
spectroscope, the lines in the spectrum are slightly 
shifted towards the red or the blue if the source emit- 
ting the light and the spectroscope receiving it are 
moving away from or towards each other. This 
principle was applied by Sir William Huggins to 
determine the velocities with which stars are appar- 
ently approaching, or receding from, the Earth. Now, 
if the Earth's orbital motion is at one time of the 
year directed towards a star, it will six months later 
be directed away from it. At the first of these times 
spectroscopic observations give the velocity of the star 
aw r ay from the Solar System diminished by the velo- 
city of the Earth in its orbit. Six months later they 



9 8 ASTRONOMY 

give the velocity of the star added to the velocity of 
the Earth. The difference of the two results is twice 
the velocity of the Earth in its orbit. Thus w 7 e find 
how fast the Earth is travelling, and as we know that 
it completes its journey in one year, the length of that 
journey can be found, and the Sun's distance derived. 

Gravitational Methods. — There are at least three other 
ways of determining the Sun's distance. One de- 
pends on the fact that the Earth every month describes 
a small circle about the centre of gravity of the Earth 
and Moon, and this slightly affects the direction in 
which we see the Sun. A second arises from the fact 
that when the Moon is between the Earth and Sun, 
the attraction of the Sun upon it is greater than when 
the Moon is on the side of the Earth away from the 
Sun. The effect of this can be traced in the Moon's 
motion, and leads to a determination of the Sun's 
distance. A third method depends on a disturbance 
which the Earth makes in the elliptic motion of 
Venus about the Sun : this leads to a determination 
of the Earth's mass, and through it of the Earth's 
distance. 

The Sun's distance may therefore be found in a 
variety of ways. The methods may be classified as 
(i) surveyor's or trigonometrical methods applied to 
the nearest of the planets; (ii) methods which take 
the velocity of light as known, and compare the 
Earth's velocity with it, or else find directly the time 
light takes to travel the Sun's distance; and (iii) by 



THE SUN'S DISTANCE 99 

effects due to gravitation seen in the motion of the Sun, 
Moon, and especially of Venus, in which the Earth's 
distance from the Sun enters as a factor. The sur- 
veyor's or trigonometrical method applied to minor 
planets when nearest to us is the simplest, and at 
present gives the best results. But it is important to 
use as many methods as possible based on different 
principles in determining what is the astronomer's 
standard of length, in terms of which he measures all 
other celestial distances. 



h 2 



CHAPTER VI 

THE SUN 

We think of the Sun as the centre and seat of 
government of the planetary system, and particularly 
as the source from which the Earth derives the heat 
and light required for the existence of man upon its 
surface. But we may also regard the Sun as a star 
much nearer to us than any of the others. For the 
stars are suns at such great distances that in the 
largest telescopes they appear to be only bright 
points. If the Sun were a million times as far away, 
we should see it as a star of the* third or fourth magni- 
tude in no respect specially remarkable. Owing to 
its proximity, a more detailed knowledge can be 
obtained of the Sun than of other stars, and it there- 
fore serves as the sample by which we judge of them. 
Both on account of its relationship to our planet and 
ourselves, and of its being the representative of the 
millions of stars in the sky, the Sun is a supremely 
interesting subject for study and research. 

Size.— When the distance of the Sun has been deter- 
mined there is no difficulty in finding its size and mass. 
If we draw lines to two points at the opposite extrem- 
ities of a diameter of the Sun, the angle between these 



THE SUN 101 

lines will be rather more than half a degree. It 
follows from this that as the Sun's distance is 93 
million miles, its diameter is 865,000 miles, or about 
no times that of the Earth. Its volume will, there- 
fore, be no cubed, or 1,331,000 times that of the 
Earth. 

Mass. — The Sun's mass is determined from the effect 
of its gravitation. The Earth describes a circle of 93 
million miles radius in one year. It follows that in one 
second it is pulled inwards from the tangent by Ti)oth 
of a foot. In Diagram LII, S being the Sun, 
E the Earth, and EG the distance travelled 
in one second, then FG = T ^ ft. Now the 
Earth's gravitation causes a stone to fall 
16 ft. in the first second after it is dropped. 
At the Sun's distance the stone would fall 
J 6 x (mI^ooo) 2 ft. = -gV x one millionth m ^ JJL 
of one foot. 

Thus the Earth's attraction would only produce 
swoooth of the effect produced by that of the Sun, 
and consequently the Sun is 330,000 times as massive. 

Density. — As the ratio of the Sun's volume to that 
of the Earth is much greater than the ratio of their 
masses, it follows that the Sun is much less dense 
than the Earth. The figures are T ;Wf°o°w or about \. 
Now the Earth's mean density is 5J times that of 
water; therefore the mean density of the Sun is only 
if times that of water, or about half the mean density 
of rocks at the Earth's surface. The pressure inside 



102 ASTRONOMY 

the Sun caused by the mutual gravitation of so huge 
a mass is enormous. The low density shows that the 
enormous pressures are accompanied by extremely 
high temperatures, and that the matter in the body 
of the Sun is in a gaseous condition. 

Solar Radiation. — The Sun is constantly radiating 
its heat into space. A very small portion of this is 
intercepted by the Earth and planets. What becomes 
of the rest we do not know. The rate at which this 
radiation is proceeding can be measured by finding 
how much heat falls each minute on a given area 
exposed perpendicularly to the Sun's rays. An 
instrument for measuring the amount of heat received 
from the Sun is called a pyrheliometer. Such an 
instrument is constructed so that it shall retain all 
the heat which falls on it from the Sun, and it is 
shielded from receiving heat in other ways. As a 
great deal of heat is absorbed by the Earth's atmo- 
sphere, allowance is made for this, and when possible 
observations are made at a high altitude, such as 
Pike's Peak or the Gorner Grat, where less atmo- 
sphere has been traversed. The " solar constant" is 
the name given to the quantity of heat which would 
be received per minute on a square centimetre 
( T 4 o inch x T 4 F inch) exposed perpendicularly to the 
Sun's rays if there were no atmosphere. Experiments 
show that this is 2*25 calories, or sufficient to raise the 
temperature of one cubic centimetre of water by 2*25° 
Centigrade. 



THE SUN 103 

If we imagine a sphere with the Sun as centre and 
a ra3ius of 93 million miles, every square centimetre 
of the surface of this sphere receives each minute 2*25 
calories. All this heat is radiated from the Sun's 
surface. Now the surface of the Sun is only T6 ^ 00 th 
part of the surface of a sphere whose radius is 93 
million miles. Consequently the Sun must radiate 
heat at the rate of 2*25 x 46,000 calories per minute 
per square centimetre, or more than 100,000 calories. 
Every square centimetre of the Sun is turning out 
work at the rate of an 11 -horse-power engine. Pro- 
fessor Young illustrates the immense output as 
follows : — if the Sun were frozen over completely to 
a depth of fifty feet, the heat emitted is sufficient to 
melt the whole of this in one minute of time. The 
mechanism by which this radiation is maintained is 
a constant flow of heated matter from the interior to 
the surface of the Sun, and a corresponding flow 
inwards of the cooled matter from the surface. Prof. 
Schuster gives an idea of the magnitude of the pro- 
cess as follows : — In every second a fresh layer of hot 
gaseous matter will have to be brought to the surface, 
a layer a quarter of a mile thick if the gas is at atmo- 
spheric pressure. And the matter brought up in the 
preceding second must be got out of the way when it 
has parted with all its heat. 

Maintenance of Heat— How is the Sun able to con- 
tinue this prodigal expenditure of heat? It cannot 
be by combustion, for if the Sun were made of coal, 



104 



ASTRONOMY 



the heat obtainable would not be sufficient to main- 
tain this expenditure for more than 6000 years, and 
geology teaches us that the Earth has been receiving 
heat from the Sun for millions of years. But every 
time a meteorite falls into the Sun it contributes heat, 
for the velocity of a body pulled into the Sun from 
a great distance will approach 400 miles a second, 
and the energy of such a body will by the collision 
be turned into heat. Though some heat is doubtless 
acquired by the Sun in this way, calculation of the 
amount shows that it is probably only a small per- 
centage of the total. Helmholtz showed that the slow 
contraction of the Sun under the influence of its own 
gravitation would supply a much larger amount. 
This process is essentially similar to that by which 
a meteorite falling into the Sun contributes to its 
heat. In the case of a meteorite, the motion of a 
small body is checked suddenly. In that of the con- 
traction of the Sun, a very large mass is continuously 
forcing its way inwards. In both cases energy ac- 
quired by gravitation is converted into heat. Helm- 
holtz showed that if the Sun's radius contracted one 
mile in 40 years, sufficient energy would be obtained 
to supply the output by radiation. It would be 
thousands of years before such a small shrinkage 
could be detected. Still, this process cannot go on 
for ever, and if the Sun has no other way of 
replenishing its stores, the Earth will not continue 
to receive the amount of heat necessary for the 



THE SUN 105 

support of life on its surface many million years 
longer. 

We may also ask how long the Sun has been 
radiating heat at this tremendous rate. Supposing 
the Sun to have been formed by matter falling to- 
gether from very great distances, the supply of heat 
thus generated would be sufficient to maintain the 
present rate of radiation for 18 million years. We 
cannot say that this is the only way in which the 
Sun has obtained heat. It is known, as we shall see 
later, that helium exists in the Sun. Now, helium is 
formed from the disintegration of radium, a process 
which is accompanied with a great liberation of heat. 
The Sun's heat may have been partly acquired in 
this way, or in others of which we know nothing. It 
is generally believed by scientists that the Earth has 
been receiving heat from the Sun for a much longer 
period than 18 million years. 

Temperature. — Very different estimates have been 
formed of the temperature of the Sun. It is seen to 
be very high because with a very powerful burning- 
glass all metals can be liquefied and vaporized. The 
difficulty in determining the temperature has been 
principally due to want of knowledge of the law con- 
necting the amount of heat radiated with the tempera- 
ture of the radiating body. In 1879 Stefan enunciated 
the law that the radiation varies as the fourth power of 
the temperature reckoned from absolute zero, or — 273 
Centigrade, Messrs, Wilson and Gray heated a 



106 ASTRONOMY 

definite surface of platinum electrically to a known 
temperature, and compared the heat radiated by this 
with the heat radiated by the Sun. Making necessary 
allowances for the amount of the Sun's heat absorbed 
in the Earth's atmosphere, they were in this wa)' 
able to determine the Sun's temperature. The results 
formed by different observers agree in giving the 
temperature of the Sun at from 6ooo° to io,ooo° 
Centigrade. 

The Spectroscope.— During the last 50 years our 
knowledge of the Sun and stars has been extended in 
unexpected directions by spectrum analysis. Just as 
the ear can detect and separate several notes of a 
piano played simultaneously, so the spectroscope 
analyzes the vibrations which are transmitted in a 
beam of light. A beam of light may be, and often is, 
extremely complex, but by this analysis the different 
notes, so to speak, are separated, and a great variety 
of information is in certain circumstances obtained of 
the source from which the light proceeds. If a beam 
of sunlight be allowed to fall on a prism, it is split 
up into a coloured band in which the colours are 
arranged in the order violet, indigo, blue, green, 
yellow, orange, red. Each gradation of colour cor- 
responds to a particular length of wave and time of 
vibration of the light — the whole consisting of an 
infinite number of different waves. A much more 
perfect analysis of a beam of light is obtained as 
follows : the light of the Sun (for example) is made 




THE SUN 107 

to pass through a very narrow slit A in the focal 
plane of an object glass B (Diagram LIII). The light 
falls on B and 
emerges as a 
parallel pencil of 
rays. This falls 
on the prism C, ^< 
whose edge is 
parallel to the 

slit A. All the rays of any one wave-length emerge 
in parallel directions from the prism, and, falling on 
the object glass D, are brought to focus. The rays 
of each colour are brought to a different focus, and 
a coloured band rv, called a spectrum, is formed. 
When this experiment is carefully performed, the 
bright band is found to be crossed by a large number 
of dark lines. 

If, instead of sunlight, the light from a Bunsen 
burner in which some sodium chloride (common salt) is 
sprinkled is admitted into the spectroscope, two bright 
yellow lines are seen, and these two lines are coinci- 
dent in position with two of the dark lines in the solar 
spectrum. The light from other substances when 
vaporized gives bright lines characteristic of the 
substances emitting them. The relation between the 
spectra of sunlight and of light from terrestrial 
sources was explained and developed by Kirchoff. 
He found that when sunlight streamed through a 
flame in which salt had been sprinkled into the 



108 ASTRONOMY 

spectroscope, the yellow lines disappeared, being com- 
pletely swallowed up by the solar dark lines which 
coincided with them in position, and which were 
much stronger than w T hen the sunlight had not passed 
through the flame containing sodium vapour. He 
was thus led to explain the existence of the two dark 
lines in the solar spectrum which coincide in position 
with the yellow lines given out by the vapour of 
sodium, by saying that light from the hot interior of 
the Sun passed through a layer of lower temperature 
at the Sun's surface in which there was the vapour of 
sodium ; that the sodium vapour in this layer absorbed 
the vibrations of the same period as those it could 
itself emit, just as a tuning-fork responds when its 
own note is played on a piano. He verified this pro- 
position experimentally in his laboratory, by allow- 
ing light containing sodium vapour from a flame at 
a high temperature to pass through a flame at lower 
temperature also containing sodium vapour before 
entrance into the spectroscope. The yellow lines 
from the flame at lower temperature were darkened. 

Spectra are of three kinds — 

(i) Continuous coloured bands with no dark lines. 
These are given by the light emitted by glowing 
solids or liquids or gases subjected to great pressure. 

(2) A number of definite bright lines. These 
spectra are obtained from glowing matter in a gaseous 
condition. They may be produced by volatilizing 
metals in flames or the electric arc; from an electric 



THE SUN 109 

spark, in which cases matter from the terminals is 
carried across the gap between them ; or by an electric 
discharge in vacuum-tubes containing a small quantity 
of such gases as hydrogen, nitrogen, etc. 

(3) Absorption spectra. These consist of bright 
bands traversed by dark lines. They are formed when 
light from a source at higher temperature passes 
through a medium containing glowing vapours which 
would themselves yield a bright line spectrum. The 
spectrum is the reversal, dark lines for bright, of that 
which would be given by the medium through which 
the light passes. 

Solar Chemistry. — Kirchoff's discovery was the 
beginning of solar and stellar chemistry. The spec- 
trum of the Sun was carefully mapped by him, and 
the positions of certain dark lines shown to be 
identical with those in the spectra of sodium, calcium, 
magnesium, barium, iron and nickel. Sunlight has 
therefore traversed a layer surrounding the Sun in 
which vapours of these elements exist. To make sure 
of the exact coincidence in position of the solar lines 
and those of terrestrial elements it is necessary to 
spread out the spectra as far as possible. This is done 
by having a number of prisms instead of one, or, still 
better, by using a " grating'' instead of prisms to 
disperse the light. A "grating " consists of a polished 
surface on which a large number of equally spaced 
parallel lines are ruled by a diamond. The art of 
ruling gratings was brought to great perfection by 



no 



ASTRONOMY 



Rowland of Baltimore. A typical grating of Row- 
land's is of speculum metal 6 inches long by 4 inches 
high, and on it are ruled 14,468 lines to the inch, so 
that altogether the grating contains 86,800 minute 
furrows. When light falls on such a surface, part 
of it is dispersed into a series of spectra. 

With gratings of his own construction Rowland 
made a magnificent catalogue and map of the lines in 
the solar spectrum. It extended from the red end of 
the spectrum through the yellow, green, and blue far 
beyond the violet. The human eye is not sensitive to 
the rays of ultra-violet light, but the spectra can be 
photographed, as photographic plates are very sen- 
sitive to this light. Altogether he measured the in- 
tensities and positions of 16,000 lines and mapped 
them. Diagram LIV shows a small part of Rowland's 



5160 



SiJO 



5184 



ftir 
4 



ML 



5fio 



SZOO 






r* r* 






Diag. LIV. 

map in the green part of the spectrum, many very faint 
lines being omitted. The numbering gives the length 
of the waves of light belonging to that exact colour. 



THE SUN in 

Thus 5 160 stands for 5 160/ 1 o 10 of one metre, or, approxi- 
mately, *oooo2 of one inch. The chemical origin of 
the separate lines is given with them : C, carbon ; Fe, 
iron; Cr, chromium, etc. By comparison with the 
spectra of terrestrial elements a very large number, 
in fact, nearly all the more intense lines in the solar 
spectrum, have been identified, and their origin traced 
to the existence in the Sun of some chemical element 
with which we are familiar on the Earth. More than 
2000 lines in the solar spectrum arise from the pre- 
sence of iron. The Sun contains hydrogen, oxygen; 
carbon, silicon; sodium, potassium, magnesium, cal- 
cium, strontium, barium; aluminium, chromium, 
iron, nickel, cobalt, manganese; lead, zinc, tin, 
copper, silver, palladium ; titanium, vanadium ; scan- 
dium, ytrium, zirconium, lanthanum, cerium, 
erbium, yterbium, europium, neodymium, gallium, 
and some other rare metals. The principal elements 
which have not been found in the Sun are nitrogen, 
phosphorus, sulphur, fluorine, bromine, chlorine and 
iodine, but, as Professor Rowland says, we cannot 
infer the non-existence of these substances in the 
Sun. In some instances their spectra do not con- 
tain any very strong lines, and their discovery is 
rendered difficult. It seems remarkable that rare 
metals, such as scandium, which it is difficult to pro- 
cure on the Earth, should make their presence in the 
Sun so plainly visible. 

It must be added that not all the dark lines in the 



11.2 



ASTRONOMY 



solar spectrum are caused by absorbing gases in the 
Sun's surface. The Earth's atmosphere in certain 
parts of the spectrum absorbs certain special rays and 
causes additional dark lines. These are mainly 
caused by oxygen and water vapour, and are specially 
prominent when the Sun at the time of observation 
is low, so that its light has traversed a long path in 
the Earth's atmosphere. 

The Sun's Surface. — To observe the Sun at the tele- 
scope precautions must be taken by suitable eye-pieces 
to cut down a great part of the heat and light. The risk 
of accident to the eye may be avoided and an equally 
good observation obtained by drawing out the eye-piece 
of the telescope a short distance and projecting an image 




TeJescope- 



3 



Diag. LV. 



of the Sun on a screen. This was the method adopted 
by Carrington, who made an extensive series of ob- 
servations upon sun spots during the years 1853-61 . It 
is more usual now to photograph the Sun, enlarging 
the image formed by the object glass by means of a 
second lens. Besides giving a larger picture, this 
has the advantage of diminishing the brightness of 
the image. Even then it is necessary to give very 
short exposures and to use very slow plates. Photo- 
graphs of the Sun are taken daily at Greenwich, the 



THE SUN 



"3 



gaps caused by cloudy weather being filled in by 
photographs taken in India. A copy of one of the 
Greenwich photographs is reproduced here. 




Diag. LVI. — Photograph of Sun. 



This photograph shows that the light of the Sun 
is more intense near the centre of the disc than at the 
edge, pointing to an absorbing smoky atmosphere 
surrounding the photosphere, or luminous body of 
the Sun. The light from near the limb passes through 
a greater depth of this layer — just as near sunset on 
the Earth the sunlight traverses a greater extent of the 
Earth's atmosphere. This "dusky layer" absorbs 
violet and blue light to a greater extent than yellow 
i 



1 1 4 ASTRONOMY 

and red, and if it did not exist, the Sun, instead of 
being yellow, would have a bluish tinge. 

Apart from the spots sometimes seen on it, the 
Sun's surface presents a mottled appearance. Nasmyth 
compared the appearances to willow leaves, Langley 
and Janssen to rice grains. These "rice grains " are of 
perhaps 400 miles diameter. They rapidly change 
their form. It is far from certain what thev are. 




Diag. LVIL— Granules on Sun. 

Langley regarded them, and his view appears to be 
shared by Prof. Hale, as the tops of long columns in 
which the heated matter from the Sun's interior rises 
to the surface. 

Observations of these curious granules have been 
made recently by M. Hansky, and still later by M. 
Chevalier. They found that on photographs taken 



THE SUN 115 

in quick succession individual granules could be 
recognized. They appeared to be moving about at 
random with velocities of from 5 to 20 miles a second. 
As M. Chevalier points out, it is difficult to believe 
that what we see arises from real horizontal move- 
ments. He compares the white granules to the sum- 
mits of waves on a choppy sea. The white tops 
move, but the particles of water which form them are 
changing all the time. 

Sun-spots. — Sun-spots were one of the first discoveries 
of Galileo's telescope. Occasionally a spot is large 
enough to be seen through dark glass with the naked 
eye. The best way of seeing them is to project the 
Sun's image, as explained on p. 112. The inner part 
of a spot, or umbra, is apparently black, and is 
surrounded by a greyer penumbra, but it must be 
borne in mind that a spot is only dark in comparison 
with the Sun. If the spot could be seen away from 
the Sun, it would be found to be brighter than an 
electric arc-lamp. Diagram LVI shows also near the 
limb bright patches, known as faculae. These faculae 
are always abundant near Sun-spots, and seem to be 
raised somewhat above the level of the photosphere. 
The nature of Sun-spots is a vexed question. They 
were for long supposed to be depressions in the Sun's 
surface, but this is not now regarded as at all certain. 

When the spectra of Sun-spots are observed, it is 

found that, as compared with the solar spectrum, 

some lines are strengthened and others weakened. 
1 2 



n6 ASTRONOMY 

These changes are doubtless due to the physical 
differences of pressure and temperature between spots 
and the generality of the photosphere, but their exact 
interpretation is not easy. Some recent observations 
seem to show that spots are of lower temperature. 
Titanium oxide was found in their spectra by Mr. 
Adams at Mount Wilson, and magnesium hydride by 
Mr. Fowler at South Kensington. The conditions 
of temperature and pressure in spots are therefore 
such as to admit of the formation of these compounds 
which do not exist in the photosphere. This certainly 
implies either a lower temperature or a higher pres- 
sure than in the photosphere, and has been generally 
interpreted as a sign of lower temperature. Some 
remarkable observations made by Prof. Hale in 1908 
show that an intense magnetic field exists in Sun- 
spots. 

Prominences and Chromosphere. — Reference has been 
made in previous chapters to eclipses of the Sun. 
At times the Moon is in such a position that 
it completely shuts out the view of the Sun for a 
few minutes from certain parts of the earth. These 
occurrences give opportunities of seeing the imme- 
diate surroundings of the Sun, which are gener- 
ally invisible to us owing to the glare produced by 
the diffusion of sunlight in the Earth's atmosphere. 
A total solar eclipse discloses two remarkable features 
of the Sun, the prominences and the corona. The 
prominences are great tongues of flame which stand 



THE SUN 117 

out from the Sun's limb, sometimes reaching to such 
great heights as 50,000 miles. Diagram LVIII shows 
one which was seen in the eclipse of 1900. The most 




Diag. LVIII. — Solar Prominences. 

important feature of the prominences is that they give 
a spectrum made up of a number of bright lines, and 
not a bright band crossed by dark lines, like the Sun. 
This was discovered in the eclipse of 1868, and estab- 
lished the fact that prominences consist of luminous 
gases, and the identification of the lines showed that 
hydrogen was one of their main constituents. The 
French astronomer Janssen, who observed this eclipse 
in India, was so impressed by the brightness of these 
lines that on the day after the eclipse he again 
examined with his spectroscope the part of the Sun 
where he had seen a great prominence, and saw the 
bright lines in full daylight. He verified that a line 
in the red was coincident with one caused by hydro- 
gen, and found a bright yellow line near to, but not 
quite coincident with, the position of the lines due 
to sodium. Sir Norman Lockyer, who was not at the 
eclipse, simultaneously discovered how these bright 
lines could be observed at all times, without waiting 



u8 ASTRONOMY 

for the rare opportunities afforded by eclipses. The 
light which hinders these prominences from being 
seen with the naked eye being diffused sunlight 
reflected by particles in our atmosphere, its spec- 
trum consists of a bright band crossed by dark 
lines. Sir Norman Lockyer argued that if he used 
a spectroscope of high dispersion, the diffused 
sunlight would be spread out into a long band of 
weak intensity, which would not obscure the spectrum 
of the prominences which is concentrated in a few- 
bright lines. By bringing different parts of the Sun's 
image tangential with the slit of the spectroscope, the 
existence of a layer all round the Sun of the same 
constitution as the prominences was discovered. To 
this the name of chromosphere was given by Lockyer. 
When the study of prominences thus inaugurated was 
carried on regularly, it was found that prominences 
were of two kinds, quiescent and eruptive. Quiescent 
prominences are generally to be found on the Sun's 
limb ; they change their form slow r ly, and are taken 
out of sight generally by the Sun's rotation. The 
eruptive prominences, on the other hand, shoot up 
with amazing rapidity, sometimes moving hundreds 
of miles per second. 

Although the chromosphere can be studied at all 
times, the moments of the beginning and ending of 
total eclipses are the most favourable. The chromo- 
sphere contains most of the elements found in the 
Sun, but there are differences between its spectrum 



THE SUN 119 

and that of the Sun which arise from the different 
physical conditions of the chromosphere and the part 
of the Sun below it where the absorption which pro- 
duces the dark lines in the spectrum takes place. 
One interesting difference is the presence of bright 
lines due to helium in the spectrum of the chromo- 
sphere, whereas there are no dark lines due to helium 
in the solar spectrum. Reference has been made to a 
bright yellow line seen by Janssen near but not co- 
incident with the lines of sodium. This line was 
found to be characteristic of the solar 'prominences 
and chromosphere, and the name helium was given to 
the unknown element which produced these lines. In 
1895 Sir William Ramsay found this element in some 
terrestrial minerals, twenty-seven years after its pre- 
sence in the chromosphere had been revealed to 
Janssen and Lockyer. 

The Corona. — The corona is of an altogether differ- 
ent character from the prominences. While the latter 
rarely extend to more than one-tenth of the Sun's 
diameter from the limb of the Sun, the corona some- 
times shows rays reaching to several diameters from 
the Sun. The instant an eclipse becomes total the 
corona is seen as an aureole surrounding the eclipsed 
Sun. It is of a pearly white colour, and brightest 
close to the Moon's dark limb. It is of a very com- 
plex form, which is only well shown by a series of 
photographs taken during the few minutes of total 
eclipse, A short exposure shows detail near the Sun, 



120 



ASTRONOMY 



while longer ones show the structure and extension at 
greater distances. Diagram LIX shows roughly the 
form of the corona in the eclipses of 1898 and iqoi. 
When the nature of the corona is investigated by 




Sun's Corona i£ 



Diag. LIX. 



Sun's Corona icjor. 



means of the spectroscope, a faint continuous spec- 
trum is found such as would be given by incandescent 
solids or liquids, and also some bright lines caused 
by glowing gases. If the light of the corona were 
to any extent reflected sunlight, then its spectrum 
would be like that of the Sun, a continuous spec- 
trum with dark absorption lines. But the exist- 
ence of absorption lines like those in the solar spec- 
trum has not been established, and we therefore 
cannot say that any considerable part of the light of 
the corona is reflected sunlight. The bright lines, of 
which more than a dozen are known with certainty, 
do not belong to any element with which we are 
acquainted. The name coronium has been given to 
the element which produces a very prominent line in 
the green part of the speetrym, lake helium j this 



THE SUN 121 

may be discovered on the Earth, but at present, at any 
rate, it is unknown. 

The Spectroheliograph. — The photography of promi- 
nences in full daylight has been developed by Prof. 
Hale and M. Deslandres. The instrument by which 
this is accomplished is called the spectroheliograph. 
A prominence is photographed by excluding all light 
except that of some definite wave-length which is 
specially characteristic of the prominence itself. Thus 
a photograph may be taken in the light of C — the red 
line of hydrogen — and such a photograph will show 
the prominences as far as they consist of hydrogen. 
Similarly, a photograph can be taken which shows 
the forms of the prominences as far as they consist 
of glowing calcium. 

The spectroheliograph has been developed further 
so as to photograph not only the limb of the Sun, but 
the whole face of the Sun in the light of one particular 
wave-length. Special interest attaches to the photo- 
graphs taken in the light of K — a line in the violet 
due to calcium vapour. In the photograph of the Sun 
on p. 113 the faculae are seen near the Sun's edge. 
The spectroscope shows that these faculae are asso- 
ciated with glowing calcium vapour. When a photo- 
graph (of the Sun) is taken in K light, a picture is 
obtained of the calcium clouds over the photosphere. 
Such photographs were found to show more than the 
f aculse, and the name flocculi (fleeces) was given tq 
them fry Prof, Hale, The illustration (Diagram LX) S 



122 ASTRONOMY 

taken from one of Prof. Hale's photographs, shows 
how ; widely these flocculi are distributed over the 
whole Sun. 




Diag. LX. — Calcium Flocculi. 

The structure of the Sun is thus seen to be ex- 
tremely complicated. The lowest part emits a con- 
tinuous spectrum; this passes through an absorbing 
layer which gives the dark Fraunhofer lines. Next 
there is a dusky layer which cuts off a great deal of 
the light, the existence of this layer being shown by 
the diminishing brightness of the Sun as we go from 
the centre to the limb. Above these are the flocculi, 
or clouds of calcium. Then we come to the chromo- 
sphere with its bright line spectrum, and outside this 



THE SUN 123 

we have the corona. In addition, there are the more 
local phenomena of spots and faculas and of the pro- 
minences rising out of the chromosphere. 

There are still two points with regard to the Sun 
which should not be omitted even in such a short 
sketch as the present, namely, (1) its peculiar law of 
rotation, and (2) the periodic fluctuations in the 
number of spots and associated phenomena. 

Rotation of Sun. — Galileo found from the movement 
of spots across the Sun's disc that the Sun rotates. 
Prolonged examination of the spots shows its axis 
to be fixed in direction, but not perpendicular to the 
ecliptic. We therefore see the Sun under a slightly 
different aspect at different times of the year. The 
axis is inclined at an angle of 7 to the perpendicular 
to the ecliptic. From June 3 to Dec. 5 the plane of 
the ecliptic is north of the Sun's equator, and thus 
for this half of the year the Sun's north pole is on the 
visible side of the Sun, and in the other half of the 
year its south pole is visible. Between 1853 an d 
1 86 1 Carrington made an exhaustive study of the 
movements of Sun-spots. He found that the Sun does 
not rotate as a solid body would, but that the period 
of rotation is greatest on the Sun's equator and 
diminishes as the poles are approached. At the 
equator a complete revolution occupies 24J days, but 
at 30 from the equator 26J days. As. Sun-spots do 
not occur at great distances from the equator, the 
slowing of the time of rotation could not be observed 



i2 4 ASTRONOMY 

in this way to greater distances than 45 north and 
south of the Sun's equator. 

In 1891 Prof. Duner determined spectroscopically 
the law of the Sun's rotation in different latitudes 
between the Sun's equator and 15 from the poles. 
The spectroscope enables the motion of bodies to or 
from the observer to be determined. The position of 
a line in a spectrum is determined by the number of 
vibrations per second which light of that exact colour 
executes. If the source of the light is moving towards 
the observer or the observer towards the source of 
light, more than the normal number of vibrations 
reach the observer each second. The position of the 
line in the spectrum is shifted slightly towards the 
blue. The amount of shift is a measure of the ratio 
of the relative movement of observer and object to the 
velocity of light. A similar phenomenon takes place 
with regard to sound. If a horn were being blown on 
a railway train which was rapidly approaching a 
station, then to a person in the station the note of the 
horn would be slightly raised. This principle (called 
Doppler's principle) was first applied astronomically 
by Sir W. Huggins to determine the velocities with 
which stars were approaching or moving away from 
the Earth. Duner applied it to determine the rotation 
of the Sun, by comparing the positions of the lines 
in the spectrum given by one end of a diameter of the 
Sun with the opposite end. He chose a part of the 
spectrum in which there are two dark lines caused by 
irgn in the Sun and also tW9 dark lines caused by the 



THE SUN 



1 






j 








j« 








*: 






* ■. i 



Diaa. LXI. 



absorbing influence of oxygen in the Earth's atmo- 
sphere. Diagram LXI shows the two spectra. The 
lines i and 3 are atmospheric, and the lines 2 and 4 
solar. The former are in the same , , x ,. 

position whatever part of the Sun the 
light comes from. The latter are 
shifted a little towards the violet if 
they come from a part which by 
the Sun's rotation is at the moment 
approaching us, and towards the red end if the light 
comes from a part of the Sun which is at the moment 
being carried away from us. The careful measure- 
ment of the distances between the lines enables the 
relative velocities of opposite ends of any diameter to 
be measured in miles per second. Observations of 
similar character were made by Dr. Halm at Edin- 
burgh and Mr. Adams at the Mount Wilson Observa- 
tory in California. The following table shows the rate 
at which the Sun is rotating in different solar latitudes — 

Lat. Time of Rotation. 

o° 24^ days 

2 ° o ° 2 5*5 

40 27*6 

6o° 29*6 

8o° 30*6 

The cause of this slowing down as we proceed from 
the Sun's equator to its poles is difficult to understand. 
There can be no doubt of its reality, for the results 
given by spots and by the spectroscope are confirmed 
by the photographs of faculae and the spectrographs 
of flocculi. Spectroscopic determinations by means of 



126 ASTRONOMY 

the hydrogen lines do not, however, show these differ- 
ences in different latitudes. The light in this case 
probably comes from a higher level, and thus gives 
the rotation of a different layer of the Sun. 

Periodicity of Sun-spots. — In some respects the 
appearance of spots on the Sun is a very irregular 
phenomenon. A spot may last for a few days or for 
several rotations of the Sun. In the latter case it will 
be visible for 14 days, then disappear owing to the 
Sun's rotation, then reappear and cross the visible 
disc of the Sun in 14 days, then disappear again, and 
so on. The number of spots on the Sun on any par- 
ticular day is not subject to any easily definable law. 
But if the average is taken for a fairly long period, 
say a year, it is seen that the number of spots fluc- 
tuates in a fairly regular manner. The same result 
holds if the fraction of the Sun's area covered with 
spots is tabulated. The following table from the 
measures made at Greenwich shows the mean area of 
spots in millionths of the Sun's visible hemisphere for 
a number of years — ■ 





Area covered 




Area covered 


Year. 


by Spots 


Year. 


by Spots. 


1889 


78 


1898 


376 


1890 


97 


1899 


III 


J891 


421 


1900 


75 


1892 


1214 


1901 


29 


1893 


1458 


1902 


63 


1894 


1282 


1903 


339 


1895 


974 


1904 


488 


1896 


543 


I905 


1191 


1897 


5 14. 


1906 


778 



THE SUN T27 

The increase in the area of the Sun covered with 
spots from 1889 to 1893 and the diminution to 1901 is 
a fair sample of a fairly regular fluctuation which has 
been traced in records of Sun-spots from the year 1610 
to the present time. Roughly speaking, Sun-spots go 
through a cycle in a period of about 11 years. 

As we have seen, spots are seldom found at more 
than 45 from the Sun's equator. On the other hand, 
they are rarely close to the equator. Their distances 
from it generally are between 30 and io°. When the 
number of spots is at a minimum, the few there are 
occur either near the Sun's equator or at a consider- 
able distance from it. As the number of spots in- 
creases the distribution changes, the number near the 
equator becoming less and less, and those at a distance 
from the equator coming rather nearer to it. 

Attempts have been made, without much success, 
to connect these changes in Sun-spots with the move- 
ments of some of the planets. A very remarkable 
connection has, however, been clearly demonstrated 
between Sun-spots and magnetic storms on the Earth, 
and with the extent of the oscillations which magnetic 
needles go through day by day. When the Sun has 
many spots magnetic storms are frequent; when the 
Sun has few T spots they are rare. This is as much 
as can be said with certainty. It does not follow that 
because there is a large spot on the Sun there will be 
a magnetic storm. It has been pointed out by Mr. 
E. W. Maunder that magnetic storms frequently recur 
after intervals of from 25 to 27 days. This is the 



i28 ASTRONOMY 

time in which by the Sun's rotation a spot is brought 
to the same position on the Sun's visible disc again. 
He is thus led to suppose that streams of electrified 
particles shot out from the neighbourhood of Sun- 
spots may reach our atmosphere and start magnetic 
storms. 

Another phenomenon related to Sun-spots is the 
form of the Sun's corona. The corona has been 
observed at numerous eclipses, and it is found that 
the forms of the corona go through a cycle in the same 
period as the Sun-spots. Two of these forms are 
illustrated on p. 120, that of 1898 being characteristic 
of a time when spots are decreasing, and 1901 when 
they are at a minimum. 

Summing up this chapter, we see that the size, 
mass, density and chemical constitution of the Sun 
are known. Its temperature is also known approxi- 
mately, and a reasonable explanation can be given 
of how its heat is maintained. Its physical constitu- 
tion presents difficult problems which have not yet 
been solved. The nature of and relationship between 
the different layers which different classes of observa- 
tion show to exist in the Sun are only very partially 
known. For the present, the law of the Sun's rotation 
and the periodicity of Sun-spots are observed facts 
for which no satisfactory explanation has been given. 



CHAPTER VII 

THE SOLAR SYSTEM 

The solar system comprises all the bodies, great 
and small, which are clustered around the Sun. They 
form a small coxmunity of their own, too far distant 
from the fixed stars to be appreciably affected by 
them, but all dominated by the attraction of the 
Sun which keeps them revolving in orbits around 
himself. The system includes the Earth, with its 
satellite the Moon, the five planets known to the 
ancients, and the outer planets Uranus and Neptune, 
with their satellites. Then there is a large number of 
small planets whose orbits lie between those of Mars 
and Jupiter. In addition there are periodic comets 
and meteor-streams, and a certain amount of finer 
matter whose existence is made apparent by the Zodi- 
acal light. 

The largest and most important members of the 
solar system are the eight planets : Mercury, Venus, 
the Earth, Mars, Jupiter, Saturn, Uranus, Neptune. 
The positions of these planets in the sky can be cal- 
culated for many centuries backwards or forwards, as 
their paths and velocities are known with great accur- 
acy. Three remarkable characteristics of them 
should be noticed — 

K 129 



i 3 o ASTRONOMY 

(i) These eight planets move in nearly the same 
plane. 

(2) The ellipses described by the planets are nearly 
circular in shape. 

(3) The planets all revolve in the same direction. 
The mean distances of the planets from the Sun 

are readily remembered in terms of the Earth's mean 
distance. They are as follows — 



Mercury 


'4 


Jupiter 


5 


Venus 


7 


Saturn 


10 


The Earth 


1 *o 


Uranus 


20 


Mars 


i*5 


Neptune 


30 



To obtain their periods use Kepler's third law, that 
the squares of the periodic times are proportional to 
the cubes of the mean distances. In the case of Nep- 
tune, the mean distance =30. The cube of 30 is 
27,000, and the square root of this is 164. The period 
is therefore 164 years. 

Minor Planets. — Between the orbits of Mars and 
Jupiter lie the orbits of the minor planets. There are a 
large number of these bodies, and every year fresh ones 
are discovered. The first of these small bodies, Ceres, 
was found by Piazzi on the first day of the nine- 
teenth century. The discoveries of Pallas, Juno and 
Vesta soon followed. These planets are just large 
enough to be seen as discs in the most powerful tele- 
scopes. The diameter of Ceres, the largest of them, 
is not far short of 500 miles, and that of Pallas, 
the smallest, about 100 miles. No more minor 



THE SOLAR SYSTEM 131 

planets were found till 1845, but since that date 
the numbers discovered annually have steadily in- 
creased, especially since photography has been used 
in the search. The total number at the end of 1900 
was 452. Since that date 200 have been added to the 
list. Most of them are extremely minute. Probably 
the larger ones have been nearly all discovered. Some 
of them, particularly Eros, have been of great use 
in the determination of the Sun's distance; one has 
served to determine the mass of Jupiter; and several 
of them illustrate interesting mathematical points in 
gravitational theory. 

It is a striking and interesting fact that these small 
planets should be confined to this particular region 
of the solar system ; Olbers suggested that they are 
fragments of a larger planet, but this explanation is 
very doubtful. 

Diameters of the Planets. — The determination of the 
size of a planet is very simple. As the planet's dis- 
tance from the Earth is known, it is only necessary 
to measure the angular diameter ^ 

seen in the telescope to deter- 
mine the real diameter. The 
angle AEB is measured and 

this value, with the knowledge of the length EA, 
gives the length AB (Diagram LXII). 

Mercury is the smallest of the major planets, having 
a diameter of 3000 miles, or f that of the Earth ; Mars 
comes next with a diameter about J, while Venus is 
k 2 



132 



ASTRONOMY 



very nearly the same size as the Earth. The other 
four planets are very much larger; Jupiter's diameter 
is ii times, Saturn's 9 times, those of Uranus and 
Neptune 4 and 5 times that of the Earth. 

Masses. — The masses of the planets which have 
satellites are readily determined from the distances and 
times of revolution of these satellites. The angular 
distance of a planet from its satellite is seen and 

measured in the telescope. 
Taking the simplest case 
where a satellite describes 
iag ' ' a circle about its primary, 

we can, as in Diagram LXIII, measure PES, the great- 
est angular distance to which the satellite goes from its 
planet. Knowing the distance EP, the distance PS 
is found. Let us call this distance a, and let the time 
the satellite takes to complete its revolution be T. If a 
is expressed as a decimal of the Earth's distance from 



the Sun, and T as a decimal of a year, then ™ will 

give the mass of the planet as a fraction of the mass 
of the Sun. This method is applicable to all the 
planets which have satellites. The masses of Venus 
and Mercury are more difficult to determine, and are 
found from the small disturbances they produce on 
the movements of one another, or of the Earth, or of 
comets which pass near them. The masses of the 
planets are generally expressed as fractions of the 
mass of the Sun. Jupiter, which is by far the largest, 



THE SOLAR SYSTEM 133 

is less than toW 11 of the Sun J Saturn comes next, 
being between a third and a quarter of Jupiter, while 
Uranus and Neptune are each about ^th. The inner 
planets are much smaller; the Earth, which is the 
largest of them, is only w oVo o th of the Sun, while 
Venus is about three-quarters of the Earth, Mars a 
little more than T Vth, and Mercury about a quarter. 

Densities. — Knowing the sizes and the masses of 
the planets, their densities are at once determined. 
The inner planets do not differ much in this respect 
from the Earth, whose density is 5J times that of 
water. The outer planets are much less dense, Jupiter, 
Uranus, and Neptune being slightly denser than 
water, and Saturn not so dense. The differences in 
density point to great difference in physical state, 
which arise from the fact that the process of cooling, 
and its accompanying process of shrinking, have pro- 
ceeded more rapidly in the small planets than in the 
large ones. 

Rotation. — The planets all rotate about their axes. 
The definite markings on Mars make its period of 
rotation easy to determine. It is rather longer than 
that of the Earth, being 24 b. 37 m. 227 s., and is 
accurately known to T Vth of a second. The periods of 
rotation of Jupiter and Saturn are determinable with 
fair accuracy, and are both not far from ten hours. 
Owing to their rapid rotation the figures of these 
planets are very oblate — so much so that the difference 
between the equatorial and polar diameters can be seen 



i 3 4 ASTRONOMY 

in a small telescope. The times of rotation of Uranus 
and Neptune cannot be given, but they are probably 
less than twenty-four hours. Owing to the absence 
of definite markings on Mercury and Venus, their 
periods of rotation are not known with certainty. 
The opinion was held for a long time that they rotated 
in about twenty-four, hours, but about twenty-five 
vears ago a very careful examination was made by 
Schiaparelli, who detected some very faint markings. 
He concluded that both planets rotate very slowly, so 
slowly, in fact, that they always present the same 
face to the Sun. Schiaparelli's results have been con- 
firmed by Lowell. Both these observers have ob- 
served the planets assiduously under the most favour- 
able conditions nnd in the best of climates. Attempts 
have been made to determine the rotation by spec- 
troscopic observations, but no decisive results have 
yet been obtained in this way. 

Satellites. — The discovery of the satellites belong- 
ing to the various planets of the solar system has pro- 
ceeded from the time of Galileo to the present time. 
As telescopes have become more powerful, fainter 
satellites have been discovered. As far as we know, 
Mercury and Venus have no satellites. The Earth has 
its one satellite, the Moon, which revolves round its 
axis in one month, and in consequence always turns 
the same face to the Earth. Mars has two very small 
satellites, whose diameters are not more than 6 or 7 
miles. They were discovered in 1877 by Asaph Hall 



THE SOLAR SYSTEM 135 

with the large refracting telescope of the Washington 
Observatory. These satellites, which are named Phobos 
and Deimos, are very near to Mars, their distances 
being only 5800 and 14,600 miles respectively, while 
the diameter of the planet itself is 4200 miles. They 
necessarily revolve very rapidly, their periods being 
7I1. 40 m. and 30 h. 18 m. It is interesting to notice 
that Mr. Lemuel Gulliver relates that the astronomers 
of Laputa "have discovered two lesser stars, or satel- 
lites, which revolve about Mars, whereof the innermost 
is distant from the centre of the primary planet exactly 
three of his diameters, and the outermost five ; the 
former revolves in the space of ten hours, and the latter 
in twenty-one and a half; so that the squares of their 
periodical times are very near in the same proportion 
with the cubes of their distance from the centre of 
Mars, which evidently shows them to be governed by 
the same law of gravitation that influences the other 
heavenly bodies. " 

The four large satellites of Jupiter were discovered 
by Galileo in 1610. They can be easily seen with an 
opera glass, and with a small telescope their transits 
in front of Jupiter and their eclipses in his shadow 
can be watched. The smallest is nearly as large as 
the Moon, and the largest has a diameter nearly half 
that of the Earth. The nearest is as far from Jupiter 
as the Moon is from the Earth, and the farthest 4J 
times this distance. Their periods round Jupiter are 
T f> 3i> 7i an d i6| days. A fifth and extremely small 



136 ASTRONOMY 

satellite was discovered by Mr. Barnard with the great 
telescope of the Lick Observatory in 1892. This little 
body is nearer to the planet than the four large 
satellites, and revolves in 12 hours. It can only be seen 
with the largest telescopes. In December 1904 a sixth 
satellite, and in January 1905 a seventh were found 
photographically by Mr. Perrine at the Lick Observa- 
tory. They are very small, and are a long way from 
Jupiter, revolving in 251 and 265 days. An eighth 
satellite, still fainter and more distant, was discovered 
photographically by Mr. Melotte at Greenwich in 
February 1907. This satellite's distance from Jupiter 
varies from 10 million to 20 million miles; its period 
is two years, and its direction of revolution is opposite 
to that of all the other satellites. 

Saturn presents a new feature in its ring. This was 
a great puzzle to the early astronomers with poor 
telescopes, who saw Saturn with what seemed like 
wings, which, moreover, changed their appearance 
and were sometimes invisible. Huyghens made out 
clearly in 1655 that Saturn's strange appendage was a 
luminous ring in the plane of the planet's equator, 
nowhere touching the planet, and extremely thin. 
The plane of this ring, like the plane of the Earth's 
equator, remains always in the same direction, and is 
inclined at an angle of nearly 27 to the ecliptic. Now, 
Saturn makes its revolution round the Sun in 29J 
years. Like the Earth, Saturn has equinoxes and 
solstices, and the Sun's position changes from 27° 



THE SOLAR SYSTEM 



137 



north to 27° south of its equator. When the Sun is 
north of the equator, the north side of the ring is 
illuminated; when south, the south side; while when 
the Sun is on the equator, only the edge of the 
ring. The ring is so thin that it is invisible to 
us when the Sun is in such a direction that it only 
shines on the ring's edge. Generally the Earth and 
Sun are both north or both south of the ring, but it 
mav happen, near the time when the Sun passes from 
north to south, that they are on opposite sides, in 
which case the ring is also invisible. A division in 




Diag. LXIV. — Saturn. 

the ring was discovered by Cassini in 1675 separating 
it into two, and in 1850 it was seen to be con- 
tinued on its inner rim by a "dusky" ring. The 



138 ASTRONOMY 

nature of Saturn's ring was n:ade clear by Clerk 
Maxwell in 1856. He showed that it could be neither 
a solid nor a liquid, but must consist of a swarm of 
little satellites circulating round the planet. If the 
ring were solid the outer parts would rotate faster 
than the inner, but if made of separate particles, more 
slowly. Keeler, at the Lick Observatory in 1895, put 
this to the test by determining spectroscopically the 
rates at which different parts of the ring were moving, 
and thus confirmed experimentally what Maxwell had 
proved mathematically. 

Besides its ring, Saturn has no less than ten satel- 
lites. The largest of these, Titan, was discovered by 
Huyghens in 1655. Its diameter is about 3500 miles. 
It revolves round Saturn in about 14 days, and is 
distant about 20 radii of Saturn. Four more satel- 
lites were discovered by Cassini between 167 1 and 
1684. A hundred years later, Sir W. Herschel dis- 
covered two smaller ones distant 3 and 4 radii from the 
planet. An eighth small satellite at a distance some- 
what greater than Titan was found independently by 
Bond and Lassell in 1848. A ninth was discovered 
in 1899 by Prof. W. H Pickering from photographs 
taken at Arequipa. This satellite is so distant that 
it takes one and a half years to complete its revolution. 
It moves in a retrograde direction in a very elliptic 
orbit. Still another very small satellite has been 
found by Mr. Pickering. 

Uranus, the planet discovered by Sir William Her- 



THE SOLAR SYSTEM 139 

schel in 1781, has four satellites. Two of these were 
discovered by Herschel in 1787, and the remain- 
ing two by Lassell in 1851. They are remarkable 
because they move in a plane almost perpendicular to 
the plane of the motion of Uranus round the Sun. 

Neptune has one satellite, discovered by Lassell, 
which moves in a retrograde direction in a plane in- 
clined at 35 to the plane of Neptune's motion. 

It is important to notice that the satellites generally 
move in planes not far removed from the ecliptic, 
and revolve around their primaries in the same direc- 
tion in which these revolve round the Sun. The ex- 
ceptions are the satellites of Uranus, the satellite of 
Neptune, and the small and distant ninth satellite of 
Saturn and the eighth satellite of Jupiter. 

We come now to the consideration of the physical 
conditions of the planets. What are their tempera- 
tures ? Are they solid bodies like the Earth ? Have 
they atmospheres? 

Temperatures of the Planets. — The four inner planets, 
Mercury, Venus, the Earth and Mars, receive 
most of their heat from the Sun. It is possible 
to form an idea of their temperatures from the 
consideration that the heat they receive from the 
Sun just balances the heat which they radiate into 
space. The uncertain factor in drawing definite con- 
clusions lies in our ignorance of the extent to which 
the temperatures of planets are regulated by their 
atmospheres. How greatly an atmosphere affects 



140 ASTRONOMY 

temperatures is seen at once from the small average 
difference between day and night temperature on 
the Earth. Professor Poynting, who has con- 
sidered the temperatures of the planets from this 
point of views has shown that it is very probable 
that, whether Mars has an atmosphere like the Earth 
or is like the Moon and has none, the temper- 
ature is everywhere below the freezing point of 
water. The only escape from this conclusion in his 
view is that an appreciable amount of heat is issuing 
from beneath the surface. But w r e see by comparison 
of the equatorial with the polar temperatures on the 
Earth to what an inappreciable extent the internal 
heat of the Earth modifies its surface temperature. 
There is thus no reason to suppose that the internal 
heat of Mars has any considerable effect on its surface 
temperature. The temperatures of Venus and Mer- 
cury, if they revolve round their axes and have atmo- 
spheres, are ioo° and 300° Fahrenheit respectively 
hotter than the Earth. If they revolve so as to pre- 
sent the same faces to the Sun always, then the hemi- 
spheres which look at the Sun are much hotter than 
this, and the hemispheres which look away from the 
Sun are at very low temperatures indeed. When we 
come to the major planets it would seem that their 
surface temperatures are determined by the internal 
heat of the planets themselves, rather than by the 
radiant heat received from the Sun. Jupiter is prob- 
ably at something like a red-heat, but it does not emit 



THE SOLAR SYSTEM 141 

sufficient light to illuminate its satellites when they 
are shaded from the Sun. Saturn, Uranus and Nep- 
tune are probably at higher temperatures. 

Atmospheres of the Planets. — A bright rim of light, as 
shown in Diagram LXV, which has been seen round 
the dark disc of Venus a little before it passed in front 
of the Sun at the transits of 1874 an d 1882 shows that 
the planet has an atmosphere. It would seem likely 
that both Venus and Mercury are surrounded by very 
dense clouds which hide the solid body of the planet. 
The spectra of Mercury and Venus are 
very like that of the Sun, and do not 
suggest that the light, after leaving 
the Sun, has passed through any 
absorbing atmosphere besides the 
Earth's. The explanation may be that 
the light by which we see these planets 
is reflected by high clouds, and does not traverse the 
densest parts of their atmospheres. The question of 
the atmosphere of Mars is one of great interest as well 
as one of considerable difficulty. The spectrum of 
Mars apparently shows no lines which are not in the 
solar spectrum. The question which has to be decided 
is, "Are certain lines which we know to be produced 
by absorption in the Earth's atmosphere more intense 
than can be accounted for by this terrestrial absorption 
alone ? " To answer the question the spectrum of the 
Moon, taken as far as possible under the same instru- 
mental and atmospheric conditions, is compared with 




142 ASTRONOMY 

that of Mars. Sir W. Huggins and Dr. Vogel con- 
sidered that the evidence pointed to the existence of 
water-vapour in the atmosphere of Mars, but Prof. 
Keeler at Allegheny, and Prof. Campbell at the Lick 
Observatory, found no appreciable difference between 
the spectra of Mars and the Moon, and therefore no 
direct evidence of any atmosphere. Recently Mr. 
Slipher at the Lowell Observatory has found that a 
band in the red end of the spectrum, caused by water- 
vapour, is intensified in the spectrum of Mars. Still 
more recently Prof. Campbell, observing from the top 
of Mt. Whitney, the highest mountain in the United 
States, in order to reduce as far as possible the effect 
of the Earth's atmosphere, found no difference be- 
tween the spectra of Mars and the Moon. These 
observations, made under most favourable conditions, 
prove that the Martian atmosphere must be extremely 
rare. In the spectrum of Jupiter there appears to be 
one line not in that of the Sun, pointing to a con- 
stituent of its atmosphere with which we are 
unacquainted on the Earth. The spectra of Uranus 
and Neptune show very considerable differences from 
that of the Sun, from which the inference is drawn 
that they are surrounded by dense atmospheres totally 
different from our own. 

Mars. — Mars and Jupiter are the only planets which 
show any considerable detail when carefully observed. 
Mars shows white caps at the poles which diminish 
in the Martian summer. If we take the view that Mars 
has an atmosphere like the Earth, but much less 



THE SOLAR SYSTEM 



143 



dense, containing water-vapour, these white caps 
would naturally be interpreted as snow. The rapidity 
with which they disappear is sufficient proof that they 
cannot be thick masses of ice and snow such as we 
find at the Earth's poles, but a very thin deposit of 
snow or hoar frost. The drawings by Prof. Bar- 
nard, made with the 36-inch reflector of the Lick 
Observatory, show the melting of the snow (if snow 




Diag. LXVL— Mars. 

it be) at the south pole of Mars in the year 1894. The 
features we see in Mars were for a time supposed to be 
land and seas. We may be pretty confident from the 
absence of clouds, and the. probable low temperature 
of the planet, that the dark parts are not seas, 
but solid land of a different colour. A long con- 



i 4 4 ASTRONOMY 

troversy has raged about the so-called canals, or thin 
lines, first discovered by Signor Schiaparelli, and since 
delineated and mapped by Prof. Lowell. The atmo- 
spheric conditions of both these observers have given 
them opportunities which few others possess, and they 
have devoted a great deal of time and attention to the 
study of the planet. But, on the other hand, Prof. 
Barnard at the Lick Observatory failed to see the 
" canals," although he could see (at moments when 
the atmospheric conditions were very favourable) a 
much greater wealth of detail than he could delineate. 
Prof. Barnard's observations have been confirmed by 
observers with the largest telescopes in America and 
Europe. Recently very fine photographs of Mars 
have been taken at the Mt. Wilson Observatory in 
California, and do not show the sharp thin lines 
which have been named " canals." It has been sug- 
gested that the canals are really subjective, and arise 
from the tendency of the eye to join up by lines mark- 
ings which are only seen with difficulty. 

A very small telescope is sufficient to show the 
belts of Jupiter. Diagram LXVII shows the planet 
as seen with the 36-inch telescope of the Lick Observa- 
tory, and drawn by Prof. Barnard in 1890. The 
surface of the planet is continually changing. Bright 
and dark spots appear, last a few months, and dis- 
appear. One of the most permanent features is a 
large red spot which appeared in 1878, and continued 
without much change of brightness till 1888, when it 



THE SOLAR SYSTEM 145 

became much fainter, but recovered its distinctness in 




Diag. LXVIL— Jupiter. 

1890, and still more in 1891- It has since grown 
fainter again, but was just visible in 1907. 

Observations of spots show that the velocity of 
rotation of Jupiter, like that of the Sun, varies in 
different latitudes. The following table and diagram 
is given by Mr. Stanley Williams. 

Latitude. Period of Revolution. No. of Spots observed. 

+ 6o°to+25° 9 h 55m 39*43s 9 

+ 25 to + io° 9I1 55m 39*92s 15 

+ io° to o° gh 50m 23*88s 27 

o° to - 12 9I1 50m 27*853 21 

- 16 to - 28 gh 55m 8*2s 1 

- 28 to -45° 9I1 55m o*9s 2 
Red Spot gh 55m 40*585 — 

L 



146 



ASTRONOMY 



The large and sudden difference between the velo- 
city of the equatorial current and the currents in the 
adjacent zones is most remarkable. A difference of 5 m. 



Surface Currents of Jupiter in 18 
south 




■ ■ • _ ■■»-..-.■•■- ■.. *•■«-. — .: ,-, •*»—',• > 



R = 9 55 39 




Southern Current. 

S. Temperate Current 
Red Spot Current. 
equatorial current 

N Tropical Current 
Northern Current 



Diag. LXVIir. 

in the time of rotation means a difference of velocity 
of the adjacent currents of more than 200 miles an 
hour. Jupiter is clearly not a solid body, and it would 
be easier to explain this great difference of velocity on 
the assumption that it is gaseous rather than liquid. 
But the permanence of the red spot is favourable to 
the view that Jupiter is liquid. The spot seems to be 
of the nature of an enormous floating island, the base 
of which extends down into the denser or more solid 
regions of the planet. 

The Moon. — Our knowledge of the Moon is far more 
extensive and certain than our knowledge of Jupiter 
and Mars. It is more than 100 times nearer than Mars, 



THE SOLAR SYSTEM 147 

and with the highest magnification of our telescopes 
can be seen as it would appear to the naked eye at a 
distance of about 200 miles. At this distance a circle 
a mile and a half in diameter would appear as large 
as the whole Moon does at its distance of 240,000 
miles, so that towns, lakes, etc., if they existed on the 
Moon, could be distinguished. The most conspicu- 
ous features on its surface are the craters. Some of 
these are 50 to 100 miles in diameter, and frequently 
have a small peak in the centre. They can be well seen 
with a small telescope. The best time to look at the 
Moon is when it is nearly half-full ; near full-moon the 
Sun's illumination is too direct to produce shadows, 
and there is not sufficient contrast for the details of the 
surface to be seen. Besides the craters, there are moun- 
tain ranges and the flat plains which Galileo named 
seas. The surface of the Moon has been very carefully 
mapped and studied, and in recent years very beautiful 
photographs, capable of a large magnification, have 
been taken, especially at the Observatory at Paris by 
MM. Loewy and Puiseux. Diagram LXIX shows 
" Copernicus," one of the most conspicuous of the 
craters, and is taken from a photograph by Prof. 
Ritchey. 

There is very conclusive evidence that the Moon 
can have but a very slight atmosphere, not more 
than one thousandth part of that which the Earth 
possesses. Moonlight when examined by the spec- 
troscope is found to be a faint copy of sunlight. 
l 2 



148 ASTRONOMY 

No absorption is found such as would occur if the 
light before reaching us had passed twice through 
an atmosphere at all comparable with that of the Earth 




Diag. LX1X. — Copernicus. 

in depth and density. The absence of any refraction 
when the Moon passes in front of and occults a star 
is further evidence that it has no atmosphere, or 
at most an extremely small one. No clouds or hoar 
frost are seen, and we therefore conclude there is no 
water. Without air and water one would naturally 



THE SOLAR SYSTEM 149 

suppose few changes to occur on the Moon's surface. 
With one very doubtful exception, none have been 
observed. 

Comets. — We have seen that Newton showed (a fact 
afterwards confirmed by Halley in a striking manner) 
that comets moved round the Sun under the influence 
of gravitation, and are therefore to be regarded — for 
the time being, at least — as members of the solar 
system. The name comet, or "hairy star," was given 
to those nebulous bodies usually possessing a tail, or 
tails, which occasionally appear in the sky for a few 
weeks or months, and then disappear sometimes for 
ever, and sometimes to be seen again after an interval 
of years. They move, as Xewton found, in highly 
elliptic orbits, in which case they return to the Sun 
after an interval of years, or in parabolic or hyper- 
bolic orbits, in which case their velocity is sufficient 
to carry them beyond the restraint of the Sun's gravi- 
tation. Since the invention of the telescope many 
comets have been found, and usually four or five are 
discovered every year. These telescopic objects are, 
as a rule, faint, insignificant, nebulous patches without 
tails. But every few T years one appears which is visible 
to the naked eye. The total number of such recorded 
during the Christian era probably exceeds 500. A few 
of these have had such bright and extensive tails that 
they have frightened beholders, who regarded them as 
portents by which 

"The heavens themselves blaze forth the death of princes.'' 



iSb ASTRONOMY 

The death of Julius Caesar and the battle of Hast- 
ings among other historical events were believed to 
have been heralded by comets. 

When a comet is examined carefully it is seen that 
it may be divided into three parts, although these parts 
run into one another so gradually that it is impossible 
to say where the exact limits between them are situ- 
ated. There is first a bright nucleus, which is merely 
a bright point in the telescope just like a star. Sur- 
rounding the nucleus is the coma, a hazy, cloudy area 
of light. It is brightest near the nucleus, and gradu- 
ally grows fainter. The nucleus and coma together 
constitute the head of the comet. Shading away from 
the head, and growing fainter and fainter till it can 
be no longer seen, is the tail. The tail streams away 
from the head in a direction opposite to that of the 
Sun. 

The most striking comet of last century was Donates 
of 1858. When discovered on June 2 it was faint and 
without a tail, and it was not till September that its 
brilliant tail developed. By the middle of October 
this stretched over nearly a quarter of the sky, being 
40 long and about io° wide in its widest part. The 
illustration (Diagram LXX) shows its naked eye ap- 
pearance. This comet may return in about 2000 years. 

By far the larger number of comets move in orbits 
not very different from parabolas, but a considerable 
fraction have an orbit which is sensibly elliptic. Such 
comets are periodic, and are seen at each return to 



THE SOLAR SYSTEM 151 

perihelion, or point of the orbit nearest to the Sun. 
Halley's comet is an instance of this class, and is 
visible at intervals of 75 years. But some have much 
shorter periods. The shortest of all is Encke's, with 




Diag. LXX.— Donati's Comet, October 1858. 

a period of three and a half years. This comet, though 
a faint one, is of special interest, as a diminution of 
its period of revolution seems to show that in its 
course it is impeded by a resistance of some kind, 
possibly of meteoric or gaseous matter. 

Halley's comet and several others have periods 
of a little over 70 years, and the furthest distance 
from the Sun to which they reach is beyond the 
orbit of Neptune. Their orbits are such that these 
comets have at some time been near to Neptune. 



i 5 2 ASTRONOMY 

Similarly, Encke's comet, and all those whose periods 
are less than eight years, move in orbits which at some 
point are comparatively near to that of Jupiter. The 
orbits of several others are related in a similar way to 
the planets Saturn and Uranus. It is clear that these 
planets have been in some way instrumental in deter- 
mining the orbits which their respective families of 
comets describe. Several hypotheses have been put 
forward to assign more definitely the parts played by 
the planets. The favourite one, though not free 
from difficulty, is that the comets which were, so to 
speak, moving past Jupiter or Neptune, as the case 
may be, were "captured" by the gravitation of the 
planet. If a comet at any time in its history passed 
very near Jupiter, its velocity might be increased or 
might be retarded. Those whose velocities w r ere suffi- 
ciently retarded would move in more restricted orbits. 

Comets are only seen when they are comparatively 
near the Sun. From their high velocities it is in- 
ferred that they travel to great distances from the 
Sun. But we cannot say with certainty that any have 
been observed to be moving sufficiently fast to get 
clear away from the solar system. The converse pro- 
position also holds that comets have not been swept 
into the solar system as it is moving through space, 
but are bodies which accompany it on that journey. 

Comets are of great volume but small mass. The 
head is often more than 1 00,000 miles in diameter. 
Nevertheless, no disturbance in the movement of any 



THE SOLAR SYSTEM 153 

of the planets or satellites has been detected in con- 
sequence of their proximity to a comet. Several have 
been near the Earth and had their movement modified 
appreciably, but yet have made no sensible modifica- 
tion in the movement of the Earth. Thus their masses 
are small compared with the Earth, probablv less than 
one hundred thousand times. We cannot say how 
much less, and measured by other standards the mass 
may be very great. If the mass were one millionth 
of that of the Earth, it would be the same as that of 
a globe as dense as the Earth and 80 miles in 
diameter. 

The spectroscope was first applied successfully to 
determine the constitution of comets by Sir William 
Huggins in 1868. He found bright bands in the spec- 
trum of the head which indicate the presence of hydro- 
carbons. These bands have since been found to be 
characteristic. In addition there is a faint continuous 
spectrum, and occasionally the dark Fraunhofer lines 
are seen, showing that a small part of a comet's light 
is reflected from the Sun. When a comet is very near 
the Sun, bright metallic lines are sometimes seen in 
the spectrum of the nucleus, especially those of 
sodium. We may infer that the nucleus of a comet 
probably consists of a collection of solid and metallic 
bodies surrounded by gaseous hydrocarbons. 

The formation of the tail is very interesting. At a 
considerable distance from the Sun a comet is usually 
a hazy, nebulous object. As it approaches the Sun 



154 ASTRONOMY 

it brightens, the nucleus becomes more distinct, 
and sends out gaseous matter in the direction of the 
Sun. This is repelled by some force from the Sun, 
and driven backwards so that a tail or tails are pro- 
duced on the side of the nucleus away from the Sun. 




Diag. LXXI. — Morehouse's Comet, 1908. 

These tails are not straight, but are curved because 
the matter driven from the nucleus shares its orbital 
motion round the Sun. The curvature is shown in 
the illustration of Donati's comet on p. 151. In recent 
years very beautiful photographs have been taken 
which show the details of the tails for a short distance 
from the head. Diagram LXXI shows a photograph of 
Comet Morehouse, taken at Harvard. The feature 
which first strikes the eye in these photographs is one 
which is irrelevant to the tail of the comet, namely, the 
short parallel lines which are strewn all over the picture. 



THE SOLAR SYSTEM 155 

They are merely the " trails " of stars which are photo- 
graphed with the comet. The camera or photographic 
telescope is kept pointing at the comet during the 
exposure, but as the comet is moving among the stars, 
the telescope is moving slightly relatively to them, 
and they come out on the photograph as short lines. 
The direction and length of the lines show the 
direction and amount of the movement of the comet 
in the sky while the photograph was being exposed. 
Some comets are seen to have several tails issuing 
from the head which change from night to night. 
In Comet Morehouse, of which an extensive series 
of photographs was made" at the Observatories of 
Greenwich, Yerkes, Heidelberg and others in 1908, 
it was seen that tails were being constantly shed and 
new ones produced. Comparison of photographs 
taken at short intervals of time showed parts of the 
tail to be moving with large and increasing velocities 
away from the comet's head. 

The movements and changes of a comet's tail are 
caused by forces in the solar system other than gravi- 
tation, and are on this account of great interest. 
The most detailed theory as yet advanced is due to 
Bredichin, a Russian astronomer, who concluded that 
the matter which issues from the nucleus of the comet 
is driven away by a repulsive force from the Sun. 
The amount of this repulsive force is not propor- 
tional to the mass of the particle of matter, but to 
the area which is exposed to the Sun. If a small 



i56 



ASTRONOMY 



spherical particle be of the right size, the repulsive 
force will just balance the attraction of gravi- 
tation. For a particle of half this radius, the repulsive 
force will be one quarter as large, but the attraction 
only one eighth ; for when the radius is halved, the 
area is one quarter and the volume one eighth as large. 
The repulsive force is thus most effective for the 
smallest particles. Bredichin examined the tails of a 
large number of comets, and found them to be of three 
types : (i) Long ones showing very slight curvature 
in a direction away from the Sun ; (ii) a 
plume-like tail curving away more 
rapidly; and (iii) a short tail curving 
away very rapidly. The curvature of 
the tail affords a means of comparing 
the repulsive forces with the attraction 
of gravity. Bredichin supposed the 
long straight tail to be composed of 
molecules of hydrogen gas ; the plume- 
like tail, which is usually the brightest 
and most important, to be composed of 
hydrocarbons ; and the short one to consist of metallic 
vapours (Diagram LXXII). 

We know of two different repulsive forces which 
the Sun may possibly exert on the matter issuing 
from the nucleus of a comet. The light radiated from 
the Sun exerts a pressure on small particles of 
amount proportional to the surface exposed to it. 
The difficulty of accepting this as the explanation lies 
in the fact that the molecules of gases are so very 




Diag. LXXIL— 

Types of Comets' 

Tails. 



THE SOLAR SYSTEM 157 

small that they escape the pressure of radiation. The 
tails would have to consist of particles one thousandth 
as small as pin-heads, but very large compared with 
the sizes of molecules. The immense size and tenuity 
of a comet's tail favours the hypothesis that it is an 
extremelv attenuated gas, and that the luminosity is 
to be regarded as a glow produced in this rarefied 
gas under electrical stimulus. This view has been con- 
firmed by spectra which have recently been obtained 
of the tails of Daniel's (1907) and Morehouse's (190S) 
comet. The spectra are made up of bright lines and 
bands, which prove the tail to consist of glowing gas 
and not of small solid particles. Spectra which appear 
to be identical with those of comets' tails have been 
shown by Prof. Fowler to be given when an electric 
discharge is passed through vacuum tubes in which 
certain gaseous compounds of carbon are present, 
when the vacuum is so high that the pressure is only 
one 50,000th of that of the atmosphere. Further, one 
of the lines has been identified by M. Deslandres with 
the principal line in the kathode spectrum of nitrogen, 
and the others bv Prof. Fowler with the kathode 
spectrum of a compound of carbon. 

Meteors. — Our views on the physical nature of comets 
have been derived from the study of meteors almost 
as much as from that of comets themselves. It be- 
comes necessary to interrupt the account of comets 
till some of the facts with respect to meteors have 
been presented. On any bright night a few minutes' 
watching will be rewarded by the sight of a shooting 



158 ASTRONOMY 

star. Sometimes a very bright one is seen by two 
observers situated in different towns. It is then pos- 
sible, from the different directions in which the meteor 
was seen when it burst out and when it disappeared, 
to calculate its height and path. In this way meteors 
are found to be at some such height as 80 to 100 miles 
when they become luminous, and to be at a height 
of about 10 miles when last seen. 

Their luminosity is caused by friction in the Earth's 
atmosphere, which they enter with velocities which 
sometimes reach 40 miles a second. A considerable 
number which have fallen to the Earth have been 
found. They consist of metallic stones, and contain 
carbon, iron, nickel and other elements with which we 
are familiar. Those which fall to the Earth usually 
weigh a few pounds, while the small shooting 
stars which are visible almost any night are dis- 
sipated into dust while passing through the Earth's 
atmosphere. 

Meteoric Showers. — It sometimes happens that on a 
particular night a large number of meteors are seen 
shooting across the sky in all directions. If the paths 
which they appear to describe as projected against 
the starry background be drawn on a globe or star 
map, it will be seen that the paths all radiate or 
diverge from a common point. This point is called 
the radiant point. The existence of a radiant point 
shows that all the meteors are moving in parallel 
directions. If, for example, meteors were falling per- 
pendicular to the Earth, their paths when drawn on a 



THE SOLAR SYSTEM 159 

globe would all pass through the zenith. The position 
of the radiant point gives the direction in which the 
meteors are moving relatively to the Earth. In Dia- 
gram LXXIII the paths of meteors observed at Green- 




Diag. LXXIII. 

wich on November 13, 1866, are plotted. It will be 
seen that they all appear to come from nearly the 
same point of the sky. 

The Leonids. — One of the most interesting of these 
swarms of meteors has its radiant point in the con- 
stellation Leo. Meteors diverging from this radiant 
may be seen on the 13th or 14th of November. 
The reason they are seen about these dates is that 
the Earth is then in a part of its orbit where these 



i6o ASTRONOMY 

meteors are to be met with. The meteors are all 
moving in nearly the same orbit round the Sun. This 
orbit and the Earth's intersect at the point where the 
Earth is situated on November 13 and 14. The key 
to the question of the cause of the November meteors 
was found in the recognition of the fact that showers 
of unusual brilliancy occurred at intervals of about 
33 years, or more exactly, three a century. A very 
brilliant shower was seen in 1833. Records inves- 
tigated by Prof. Newton of New Haven led him to 
predict a shower in the year 1866. He concluded that 
the November meteors were all moving in an orbit 
round the Sun, but that instead of straggling uni- 
formly about this orbit they were specially thick in 
one particular part. He found that there were several 
different orbits which would give rise to a specially 
brilliant shower about every 33 years. The fact that 
the date of the shower was gradually getting later, for 
it was Oct. 19 in a.d. 902, and Oct. 24 in 1202, and 
Nov. 12 in 1833, enabled Prof. Adams to decide which 
of these orbits was the true one. In this way it was 
settled that the November meteors move in an 
eccentric elliptic orbit which stretches beyond Uranus, 
and that their period is 33^ years. 

Comets and Meteors. — In 1867 it w T as shown by the 
researches of Oppolzer and Leverrier that a comet 
discovered by Tempel in 1865 moves in the same 
orbit as the November meteors. Schiaparelli showed 
that the orbit of the Perseid meteors which are seen 



THE SOLAR SYSTEM 161 

in August is probably identical with that of Turtle's 
comet of 1862. A third relationship between comets 
and meteors was shown by the strange behaviour of 
Biela's comet. This comet was discovered in 1826, 
and found to have a period approximately six and a 
half years. In 1846 this comet was seen to split into 
two, which kept at a distance of about 200,000 miles 
from each other. In 1852 the two parts were at a 
distance of two million miles. In 1859 and 1865 the 
comet was not seen, but in 1872 its place was taken 
by a shower of meteorites radiating from a point in 
Andromeda. 

We are thus led to regard a comet as made up of a 
loose collection of meteorites, gathered possibly 
around a larger central nucleus. When the comet 
approaches the Sun, heat and other radiative influ- 
ences tend to disintegrate the mass, and to drive off 
gaseous constituents. The gaseous constituents thus 
driven off form the tails. 

Nebular Hypothesis. — The Sun, with the planets and 
comets which circulate round it, forms a system so far 
from any other celestial bodies that their influence 
upon it is imperceptible. It pursues its course and 
undergoes its development entirely apart from them. 
In a famous hypothesis which he propounded in the 
Systeme du Monde, Laplace attempted to trace the 
process of its evolution. He was struck by the facts 
that the larger planets are nearly in the same plane, 
that they and their satellites revolve in the same direc- 

M 



1 62 ASTRONOMY 

tion, and that the Sun and planets are rotating in this 
same sense. These coincidences are too many to be 
the result of chance, and point to some common cause. 
He put forward the theory that a vast nebula — diffused 
tenuous matter — once extended to the confines of the 
solar system, and under the influence of gravitation 
slowly contracted. He further supposed that this 
nebula was endowed originally with a slight rotatory 
motion. As the contraction proceeded the rotation 
necessarily increased, and rings or other masses were 
thrown off which collected and formed planets. This 
theory received fresh support when it was discovered 
that heat was developed in the process of contraction. 
The existence of nebulae in the sky, and the discovery 
of their gaseous condition, which we shall come to 
in a later chapter, was regarded as fresh evidence in 
its favour. Discoveries made since Laplace's time 
have shown that there is not quite so much unanimity 
as he supposed in the directions of planets' rotations 
and the movements of their satellites. Besides this 
there are dynamical difficulties, for from the present 
state of the solar system it is possible to calculate 
the speed of rotation the nebula had when it extended 
—let us say — as far as Jupiter, and this speed is not 
nearly sufficient for any part of the nebula to have 
been whirled off. The process of evolution cannot be 
traced by following the simple principle which La- 
place enunciated. It has been pointed out recently by 
Prof. Jeans that "gravitational instability," or a tend- 



THE SOLAR SYSTEM 163 

ency of matter to accumulate around nuclei of slightly 
greater density, and for these nuclei to increase and 
gradually collect more and more nebulous matter 
around them is probably a more important cause 
than rotation in the development of a planetary system 
from a nebula. A very careful criticism of Laplace's 
hypothesis has been given by Messrs. Chamberlin 
and Moulton. They consider that the solar system 
has been derived from the aggregation of meteoric 
dust and fragments, which had possibly resulted from 
the collision of previously existing bodies. 

Sir George Darwin has attempted to trace in detail 
the birth of the Moon. He supposes that the Earth 
and Moon were once part of the same fluid body. 
Owing to its rotation about an axis this body had a 
spheroidal form. In consequence of the contraction 
caused by cooling, the speed of rotation increased and 
the body bulged out more and more at its equator till 
it reached the limit at which a spheroidal form is 
possible. As the contraction continued the form 
changed to an ellipsoid with three unequal axes, 
then to a pear-shaped figure, and finally split into two 
bodies. Large tides were generated in these bodies 
by their mutual gravitation, and the friction of these 
tides caused the tw 7 o bodies to separate further. This 
very complicated question has been mathematically 
worked out in detail by Prof. Darwin, but there are 
still some difficulties to be overcome before we can be 
certain that it is a true account of the Moon's history. 
m 2 



CHAPTER VIII 

DISTANCES AND MOVEMENTS OF THE STARS 

The last thing astronomers have learned from the 
study of the stars has been the nature of the stars 
themselves. Their vast distances make them appear 
"fixed" in the firmament, and they have served as 
reference points from which the movements of other 
bodies have been inferred and measured. Thus the 
rotation of the Earth, the movements of the Earth's 
axis, the velocity of light have all been discovered 
directly or indirectly, by the help of observations of 
the fixed stars. The fixity of the stars showed the 
movements of the planets and thus led to the Coper- 
nican system. The bright points called planets or 
wandering stars on the dome of the sky have been 
shown to be large bodies resembling the Earth which 
circulate about the Sun. Their sizes, positions and 
movements have all been determined. The "fixed" 
stars present a similar but more difficult problem. 
They appear as bright points projected on the sky. 
Can they be made to stand out in three dimensions ? 
Can the points on the sky be replaced by material 
bodies in space whose positions and movements 
relatively to the Sun are known ? Further, can the 

masses and sizes of the stars be determined? 

164 



DISTANCES AND MOVEMENTS OF STARS 165 

If the distances of stars were as easy to determine 
as their directions these questions would be simplified 
very much. As we have seen, a star's right ascension 
and declination fixes its direction, just as the longitude 
and latitude of a place on the Earth fix the direction 
in which the place would be seen from the Earth's 
centre. If the distances of the stars from the Earth 
were known as well as their directions, we should be 
at once in a position to construct a model of the 
sidereal universe so far as the positions of the stars are 
concerned. But the determination of stellar distances 
is a difficult problem which has lured and baffled 
astronomers for centuries. 

Before we approach this question, it will be con- 
venient to refer briefly to the nomenclature by w*hich 
stars are identified and to indicate what is meant by 
the magnitude of a star. 

Nomenclature of Stars. — A small number of the 
brightest stars like Sirius, Arcturus, Aldebaran have 
been given special names. Next to these come a large 
number of the stars visible to the naked eye w r hich are 
named from the constellation to which they belong, 
being distinguished either by Greek letters or num- 
bers. Bayer in his Uranometria, a star atlas published 
in 1 601, used Greek letters, the stars being arranged 
approximately in order of brightness for each con- 
stellation. Thus we have a, ft, y Leonis, etc. Flam- 
steed, the first English Astronomer Royal, made an 
accurate catalogue of the stars' positions in which he 



1 66 ASTRONOMY 

designated the stars by numbers as i, 2, 3 Leonis, etc. 
The names given by Bayer and Flamsteed have been 
generally adopted. For fainter stars the number in 
some well-known catalogue serves as a name. Thus, 
Br. 3147, Gr. 1830, and Lai. 21 185 refer to stars which 
are respectively No. 3147 in Bradley's catalogue, 
made in 1755, No. 1830 in Groombridge's catalogue 
of 1810, and No. 21 185 in Lalande's catalogue of 
1800. 

Positions of Stars in the Sky. — The direction of a 
star, if it is a bright one, can be obtained roughly from 
a celestial globe. If the accurate direction is required 
reference must be made to a star catalogue. The 
earliest star catalogue in which the positions — that 
is, the right ascensions and declinations — are 
given with sufficient accuracy for modern require- 
ments, was made by Bradley from observations at 
Greenwich about 1755. Since that time the results 
of many observations with transit circles have been 
embodied in star catalogues. Throughout the whole 
of last century, for example, catalogues giving the 
positions of the brighter stars derived from the most 
accurate observations were repeatedly made at Green- 
wich and other national observatories. One of the 
largest star catalogues, giving the accurate positions 
for the date 1875 of all northern stars as bright as the 
ninth magnitude and many fainter ones, was the result 
of the combined effort of 15 observatories under the 
auspices of the German Astronomical Society. 

Stellar Magnitudes. — The brightness of a star as seen 



DISTANCES AND MOVEMENTS OF STARS 167 

from the Earth, like its position, is a quantity which 
admits of immediate measurement. Evidently a 
knowledge of the stars' distance is required before the 
intrinsic brightness of stars can be compared. If a 
star's distance were doubled the light received from 
it would be diminished fourfold, or more generally 
the light received from equally bright stars varies 
inversely as the squares of their distances. The quan- 
titative measurement of the light received from stars 
is a comparatively recent astronomical work, which 
has been extensively pursued under Prof. Pickering's 
direction at the observatory at Harvard College, and 
by Messrs. Muller and Kempf at Potsdam. Various 
photometric methods have been devised for this pur- 
pose, and these have replaced and given precision to 
the eye-estimations previously made by astronomers. 
The brightness of a star is indicated by its magnitude, 
and the photometric scale is such that a difference of 
one magnitude between two stars corresponds to 2*5 
times the amount of light. Thus from a star of mag. 
i'o, 2*5 times as much light is received as from a star 
of mag. 2*0; while from a star of mag. 2*0, 2*5 times 
as much light is received as from a star of mag. 3*0, 
and so on. Thus the brightness or amount of light 
received from a star is related to its magnitude by a 
formula — - 

Amount of light = C x (-^ T Y\ where m is the star's 
magnitude, and C is the amount of light re- 
ceived from a star of magnitude o'o, L e. a 
star slightly brighter than Vega. 



1 68 



ASTRONOMY 



Aldebaran is of magnitude ri, or slightly fainter 
than the first, while Altair is of magnitude 0*9, or 
slightly brighter. The stars brighter than first mag- 



nitude are — ■ 










Mag. 




Mag. 


Sirius 


-r 4 


Rigel 


o*3 


Canopus 


— I'O 


Procyon 


o*5 


Vega 


O'l 


Achenar 


0:5 


a Centauri 


0*2 


/? Centauri 


o*8 


Capella 


0'2 


Altair 


0-9 


Arcturus 


03 







Thus Vega gives nearly 2*5 times the light of a 
first magnitude star, and Sirius gives (2'5) 1,5 , or 4 
times the light of Vega. 

With the naked eye stars slightly fainter than 6*o 
mag. can be seen. A very small telescope will show 
stars down to 9*0 mag., and with the largest telescopes 
the sixteenth magnitude can be reached. A convenient 
rule which connects the brightness of a star with its 
magnitude is that a difference of 5 magnitudes corre- 
sponds to a ratio of 100:1 in the amount of light 
received. 

Thus from a star of ro mag. 100 times as much 
light is received as from a star of 6*0 mag. ; from one 
of 6*o mag. 100 times as much as from one of iro 
mag., and from one of n*o mag. 100 times as much 
as from one of i6*o mag. Thus one millionth of the 
light of a first magnitude star is received from one of 
the 1 6th magnitude. 

Number of Stars. — A very interesting question natur- 
ally arises as to the number of stars of each magnitude. 



DISTANCES AND MOVEMENTS OF STARS 169 

About 1855 Argelander at Bonn made a very complete 
list of all the stars as bright or brighter than 9*5 mag. 
between the north pole and 2 south of the equator. He 
enumerated altogether 324,000 stars. This work was 
continued as far as 23 south declination by Schonfeld, 
who enumerated in this part of the sky 134,000 stars. 
From 22 u south declination to 52 south declination 
an enumeration of all stars down to io'o mag. made at 
Cordoba contains 490,000 stars. At the Cape Observ- 
atory similar work has been accomplished photo- 
graphically extending from 19 south declination to 
the south pole, giving approximate positions and 
magnitudes of 455,000 stars. The difficulty in 
researches of this class is in keeping a constant scale 
of magnitudes, as the magnitudes are necessarily 
determined by eye-estimation in visual observa- 
tions, and by what amounts to a very similar process 
in photographic observations. When corrections are 
made so that the estimates may be as far as possible 
according to the photometric scale, the following 
results are found for the total number of stars of 
different magnitudes. 



Mag. 


Nc 


>. of Stars. 


Mag. 


No. of Stars. 


>ro 




II 


6'o- 7-0 


!0,275 


I'O - 2*0 




28 


7-0- 8'o 


31,000 


20-3-0 




io 5 


8-o- 9-0 


93,000 


30-4-0 




300 


9*0 - 100 


271,000 


40-5-0 




1016 


IO'O- II'O 


710,000 


50-6-0 




3265 







Our knowledge of the immense number of very 



170 ASTRONOMY 

faint stars begins with the Herschels who counted 
the stars in sample areas in different parts of the sky. 
The limiting magnitude to which Sir J. Herschel went 
was approximately 14*0 m. The estimated number of 
stars down to this limit is nearly 24 millions. With 
some of the modern reflecting telescopes stars three 
or four magnitudes fainter than 14*0 mag. can be 
photographed, and the total number down to i8'o mag. 
may be estimated at about 1000 millions. 

The increase of the number of stars per magnitude 
is very interesting. It is seen to be roughly 3 times. 
Now, as the amount of light received from a star is oh 
times as much as that received from a star a magnitude 
brighter, it follows that as far as n'o mag. the total 
light contributed by all the stars of any one magnitude 
is greater than that contributed by the class a magni- 
tude brighter. This cannot go on indefinitely, or the 
total amount of light received from the stars would be 
infinite. The ratio of the number of stars per magni- 
tude to the number a magnitude brighter does not 
appear to fall off very fast for several magnitudes 
fainter than n'o m. 

Distance of Stars. — We have seen how the distance 
of the Moon may be determined by observing the 
difference of its direction from two points on the 
Earth's surface; and how the same method carried 
out with greater refinement enables the distance of 
Mars and of certain minor planets when nearest the 
Earth to be measured, and the scale of the planetary 
system to be derived. 



DISTANCES AND MOVEMENTS OF STARS 171 

But the distance of the stars is so vast that the 
most refined instruments show no trace of any differ- 
ences in their directions as viewed from the north of 
Europe or South Africa. Such a base-line for their 
triangulation is absolutely inadequate. When Coper- 
nicus showed that the Earth revolved round the Sun, 
astronomers realized at once that they could use a 
very much larger base-line. After an interval of six 
months the • Earth has moved from a position 90 
million miles on one side of the Sun to one 90 million 
miles on the other. With such a large base-line as 
180 million miles some differences in the directions of 
the stars which would permit of the determination of 
their distances was surely to be anticipated. Diagram 
LXXIV, which consists of rough sketches of Edin- 
burgh from two different points in the grounds of the 
Royal Observatory, shows the change produced by 
a slight difference of point of view. The church spire 
on the left, which is only half as distant as the Castle, 
is in one sketch seen projected against the right edge 
of the Castle, but in the other near the middle of it. 
The chimney on the right, which is a little nearer to 
the observatory than the crown-like spire of St. Giles' 
Church, appears in one sketch to the right and in the 
other to the left of this spire. 

But the contemporaries and successors of Coper- 
nicus could not find the slightest trace of any paral- 
lactic effect of this kind among the stars. Some 
concluded that Copernicus was wrong, others that the 
distances of the stars were so great that the distance 



172 ASTRONOMY 

of the Sun was inappreciable in comparison with 
them. As means of measuring angular positions 
were improved, attempts were renewed to find some 



Diag. LXXIV. 

small differences in the relative positions of the stars 
which would show that though very large the distances 
were not immeasurably great. Of these unsuccessful 
attempts the most notable are Bradley's, from 1729 
to 1748, which led to the discovery of the aberration 
of light and of a small oscillatory movement of the 
Earth's axis called Nutation, and Sir William Her- 
schel's, which led to the discovery of double stars 



DISTANCES AND MOVEMENTS OF STARS 173 

revolving about one another under the influence of 
their mutual gravitation. 

Before the distance of any star was actually measured 
indications were found that some of the stars though 
at great were still at appreciable distances. Halley 
found that the three bright stars, Sirius, Arcturus 
and Aldebaran, were placed in Ptolemy's catalogue 
in positions slightly to the north of those they occu- 
pied in his own time. He guarded against this being 
due to errors of Ptolemy's catalogue by observing that 
the positions of other and fainter stars agreed with 
those assigned to them by modern observations. In 
a communication to the Royal Society in 17 18 Halley 
remarks, " These stars, being the most conspicuous 
in heaven, are in all probability nearest to the Earth; 
and if they have any particular motions of their own 
it is most likely to be perceived in them, which in 
so long a period as 1800 years may show itself by an 
alteration of their places, though it be utterly im- 
perceptible in the space of a single century of years." 
Halley's conclusions were confirmed by other astron- 
omers, and in 1756 Mayer, a German astronomer, 
gave a list of 57 stars whose positions had changed 
perceptibly in half a century due to the movement of 
the stars themselves relatively to the solar system. 
At the middle of the eighteenth century it was fully 
realized that the Sun and stars were similar bodies, 
but that the stars were vastly more distant. The 
discovery of movements among them showed that, 



i; 4 ASTRONOMY 

though great, their distances were not infinite, and 
held out hopes to astronomers that with more refined 
measures these distances might be determined. 

Success in measuring the distance of a star was 
attained almost simultaneously by three astron- 
omers, Bessel, Struve and Henderson. Bessel chose 
61 Cygni, a star of only the 5th magnitude, on 
account of the rapidity of its motion across the sky. 
Near to this star were two others which did not share 
this large motion, and were presumably at a much 
greater distance. He commenced a series of measures 
with a heliometer in August 1837 an d continued them 
till October 1838. He found a very small movement 
of the star with reference to both the small comparison 
stars, analogous to the change in position shown in 
the diagram of p. 172, arising from the fact that his 
point of view was changed by the motion of the 
Earth around the Sun. He concluded that the " paral- 
lax " of 61 Cygni was o*32 /; . 

The parallax is the small angle which the radius 
of the Earth's orbit subtends at the star's distance. 

s If E (Diagram LXXV) be the 

I ___- """*"" position of the Earth, © of the 

£ Sun, and the line QS'is drawn 

Diag. LXXV. ,. « ^^ 

perpendicular to E © and carried 
till ©S represents the star's distance on the same 
scale, then the small angle ES© is called the star's 
parallax. If S© is 200,000 times E©, then the angle 
ES© will be i ;/ . Bessel found the angle to be o*32 7/ 



DISTANCES AND MOVEMENTS OF STARS 175 

in the case of 61 Cygni, and therefore 61 Cygni is 
0-V2 x 200,000 times, or more than 600,000 times the 
distance of the Sun. 

Meanwhile Struve at Pulkova had from 1835 to 
1838 been making a similar series of observations 
on the bright star Vega. This star, though not 
moving so fast as 61 Cygni, indicates, both by its 
movement and its brightness, that it is probably one 
of the stars nearest to the Sun. Struve found for this 
star a parallax of o , 26 // , indicating a distance of 
800,000 times that of the Sun. Later observations 
have shown that the parallax is not so large as this, 
but nearer to o'io", so that its distance is two million 
times that of the Sun. 

Henderson's observations were made by a different 
method. Appointed H.M. Astronomer at the Cape of 
Good Hope in 1831, he made a series of observations 
to determine the declination of the bright double star 
a Centauri. This star, which is the fourth brightest 
in the heavens, only Sirius, Canopus and Vega being 
brighter, has a very large proper motion. Henderson 
examined his observations and found that they showed 
the star to have a parallax of i /; . His calculations 
were not made till he had left the Cape on his 
appointment as Astronomer Royal for Scotland, and 
he did not announce the result till it had been con- 
firmed by observations of the right ascension of the 
same star. He published his determination of the 
parallax of a Centauri two months after Bessel had 



176 ASTRONOMY 

published that of 61 Cygni. Later and more accurate 
observations have shown that the parallax is not quite 
so large but only o'75 /; . Nevertheless this star is, as 
far as we know, our nearest neighbour among the 
stars, its distance being 270,000 times that of the 
Sun. 

The work of determining the parallax of a star is 
extremely delicate and very laborious ow T ing to the 
care which needs to be taken to obtain the necessary 
accuracy. In recent times the parallaxes of a number 
of southern stars have been carefully determined by 
Sir David Gill at the Cape. Among other stars he 
finds that Sirius has a parallax of o*37 7/ , but that 
Canopus is too far away to show any sensible paral- 
lax. The star with the largest parallax next to a 
Centauri is a faint star of magnitude 7*6, situated 
in the Great Bear. The parallax of this star is o*46 r/ . 
There are about twenty stars whose parallaxes are 
known to be greater than o*20 /; , i. e. whose distances 
are less than one million times that of the Sun. On 
the other hand, even some of the brightest stars, such 
as Canopus and Rigel, are at such a great distance 
that they show no certain parallax. The fact that 
some faint stars are comparatively near, while some 
bright ones are too far away for their distances 
to be measured with certainty, shows that there is 
very great diversity in the actual luminosity of the 
stars. If all were at the same distance some would 
appear thousands of times brighter than others. 



DISTANCES AND MOVEMENTS OF STARS 177 

It is not easy to form any conception of the great 
distances the stars are from us. If the distance 
between the Sun and Earth were represented by the 
distance between two railway lines, the distance of a 
Centauri, our nearest neighbour among the stars, 
would be 245 miles, and the distance of Sirius would 
be 500 miles. Thus if two railway lines starting from 
London instead of keeping parallel at a distance of 
4 feet 8J inches, converged so gradually that they 
met at Durham, the long triangle thus formed would 
be similar to that formed by the Sun, the Earth, and 
a Centauri. For more distant stars the triangle 
would be proportionately longer. The measurement 
of stellar distances rests on the determination of the 
small angle at the vertex of the triangle, and as 
this angle is extremely small the utmost care is 
necessary to avoid any error due to instrumental 
causes. For this reason the differential method of 
determining stellar parallaxes has generally been 
used; that is, a small change 
in the position of a star 
relative to neighbouring stars 
has been looked for. In Dia- Diag ' LXXVL 

gram LXXVI if E ± and E 2 are the positions of the 
Earth when on opposite sides of the Sun (marked © 
in the diagram), and if o- is a comparatively near star 
ando^ a distant one, then E^ and E 2 cr 1 are sensibly 
parallel, and the angle E^E^, which is twice the paral- 
lax of the star <r, is the sum of the two small angles 




178 ASTRONOMY 

o-E^ and o-E 2 o- 1 . It is easier to determine the angle 
E 1 (jE 2 accurately in this way than in any other, as the 
many causes except parallax which affect the position 
in the sky of o- as seen from E 1 and six months later 
from E 2 , equally affect the position of ar 1} but not the 
relative positions of the two stars. 

Unless the stars of reference are much more distant 
than the star whose parallax is sought, the differential 
method will fail, but if they are 10 or 20 times as 
far off the result will be T Vth or-^-th part too small. 

The stars whose distances have been satisfactorily 
determined number from 150 to 200. Those whose 
distances have been investigated are in nearly all 
cases very bright or with very large proper motions. 
The brightness and the proper motion have been 
clues which have guided astronomers in the choice 
of stars whose distances they should attempt to 
determine. This manner of selection makes it diffi- 
cult to deduce from the results correct views as 
to the average distances of stars. Prof. Kapteyn, 
realizing the importance of an increase in our know- 
ledge of the parallaxes of stars, has set on foot a 
scheme by which certain selected areas well dis- 
tributed over the sky shall be photographed at such 
times of the year that any stars of large parallax will 
be detected by their slight movements relative to the 
general mass of the stars photographed on the same 
plate. When stars of large parallax — let us say greater 
than o'i"— are picked out in this way, a great deal 



DISTANCES AND MOVEMENTS OF STARS 179 

of information will be obtained on many important 
points on which our knowledge is at present very 
scanty. For example, the percentage of stars of differ- 
ent magnitudes, having parallaxes of this amount, will 
show to what extent the apparent brightness of a 
star is due to its intrinsic brightness, and to what 
extent it is due to nearness to the Earth. Similarly 
we shall be able to judge to what extent a large proper 
motion is due to a large velocity, and to what extent 
it arises from the star's proximity to the Earth. These 
and other questions bearing on the geometry of the 
stellar system depend largely for their answer on the 
increase of our knowledge of the parallaxes of stars. 

Proper Motions of Stars. — Although only a small frac- 
tion of the stars are sufficiently near for their dis- 
tances to be separately determined, there are a large 
number of stars sufficiently near for their proper 
motions or angular motion on the face of the sky 
to be determinable. With the lapse of time the 
number will increase, for if motion cannot be detected 
in one year it may be in ten, if not in ten 
a century may be sufficient. The existence of a 
proper motion clearly shows that a star is not at an 
infinite distance, otherwise its velocity would need to 
be infinite for any change in its position to be 
produced. 

The magnitude of the proper motion does not 
enable a star's distance to be determined unless the 
actual velocity of the star is known. The study of 

N 2 



i8o ASTRONOMY 

proper motions does, however, give information 
about the average distances and movements of stars 
which are too far distant for their parallaxes to be 
determined individually. 

The proper motions of many stars have become 
known during the last quarter of a century because a 
sufficient interval of time has elapsed since the posi- 
tions of the stars were accurately catalogued for 
changes in their position to be apparent. Modern 
determinations of proper motion date from the 
revision by Dr. Auwers of the catalogue executed by 
Bradley at Greenwich in 1755 and its comparison 
with catalogues made a hundred years later. By this 
work the angular movements on the face of the sky of 
more than 3000 stars were made known. The proper 
motions of thousands of stars have since been investi- 
gated by different astronomers. As examples of the 
actual amount of stellar proper motions we may take 
the very bright stars given on p. 168. The number 
of seconds they move over the face of the sky per 
century are as follows — ■ 

Sirius 132" Capella 44" Achenar 9" 

Canopus 2" Arcturus 22S" /3 Centauri 4" 

Vega 35" Rigel o" Altair 65" 

a Centauri 368" Procyon 125" 

Canopus and Rigel show practically no movement, 
and are probably at a very great distance. As we have 
seen, attempts to determine their parallaxes have been 



DISTANCES AND MOVEMENTS OF STARS 181 

unsuccessful . It follows that their actual luminosity must 
be immense. On the other hand, Arcturus is an instance 
of a star moving with a very great velocity. Its paral- 
lax has been determined as o'03 r/ . While this is the 
small angle the distance from the Earth to the Sun 
subtends at Arcturus, its movement in a year on the 
face of the sky subtends an angle 2 , 28' / . In one year, 
therefore, it moves f'ff times the distance from the 
Earth to the Sun. This works out to be 76x93 
million miles a year or more than 200 miles a second. 
Large proper motions are not confined to bright 
stars. Till a few years ago Gr. 1830, a star of 6'g mag. 
was the most rapid known; but in 1897 a faint 
southern star of 8*5 mag. was found to be moving still 
more rapidly. The following five stars have proper 
motions greater than 500^ a century. 







Mag. 


Prop. 
Motion. 


Parallax. 


Cordoba V, 


243 


8-5 


870' 


031" 


Gr. 1830 




6-9 


704" 


0'12" 


Lac. 9352 




7"5 


694J 


CV28" 


Cor. 32416 




8-5 


607" 






61 Cygni 




57 


520" 


o'33" 



The parallaxes show that four of these five stars 
are comparatively near. The faintness of the stars is 
therefore a proof of their small absolute luminosity, 
and illustrates the great variations among the stars in 
this respect. 

Altogether about 100 stars are known to have proper 
motions of more than iqo !/ a century, and about 2000 



1&2 



ASTRONOMY 



of more than 20" a century, but the latter list is very 
incomplete. The probable number of those which 
have proper motions greater than 5" a century is 
given by Newcomb as 20,000, but the data are as 
yet insufficient for a precise estimate. 

Motion of Sun in Space. — The proper motion of a 
star may arise from its own motion or from a motion 
of the solar system in space. In the former case there 
is, a priori, no reason to expect any regularity among 

the proper motions; but in the 
latter case there would be a 
general drift of the stars in an 
opposite direction to the move- 
ment of the solar system. In 
Diagram LXXVII let O be the 
centre of a large circle, and let 
O move a small fraction of the 
Diag. lxxvii. radius to O' in the direction 

OG. The direction in which A is seen has 
changed from OA to ; A; A has apparently moved 
in the direction of the arrow through an angle 
COA— CO ; A or OAO 7 . Similarly E has apparently 
moved through an equal angle. G and C, which 
are in the direction of and the direction opposite to 
the movement of O, have not changed their directions 
at all. A point B has apparently moved through an 
angle COB — CO'B or OBO ; . This angle is largest 
when B is like A or E, perpendicular to OO 7 , and 
becomes smaller as B approaches C, the point from 




DISTANCES AND MOVEMENTS OF STARS 183 

which O is moving or the point G to which O is 
moving. If, instead of dealing with a circle, w T e 
take a sphere like the sky, the apparent angular 
movement of the stars arising from the real movement 
of the Sun (carrying the Earth with it) will be towards 
the point from which the Sun is moving. The move- 
ment will be imperceptible in stars near this point or 
180 away from it, and will be largest for those 90 
distant. There are two complications when this geo- 
metrical conception is applied to the stars. First, 
part of a star's proper motion arises from the star 
itself; and secondly, the unknowm and irregular dis- 
tances of the stars prevent the effect from being as 
regular as in the geometrical illustration just given. 
One of Sir William Herschel's greatest discoveries 
was his perception of a certain amount of regu- 
larity in the proper motions of stars, and his 
attribution of this to a translation of the solar 
system in space towards a point in the sky which 
he fixed in the constellation Hercules near the star 
A Herculis. 

Herschel's first determination of the direction of 
the solar motion was made in 1783. He obtained 
from very little material a result in very good agree- 
ment with modern determinations. He made a new 
determination in 1805, an d found for the Sun's apex 
or point towards which the Sun is moving a position 
30 distant from A Herculis. This discordance led some 
astronomers, and among others Bessel, to doubt 



1 84 ASTRONOMY 

whether a movement of the solar system had really 
been established. 

In 1830 Argelander made very exact observations 
of a number of bright stars. He compared the posi- 
tions of 390 of these with those found by Bradley 
in 1755. The interval of 75 years between the obser- 
vations provided him with a very considerable change 
of base — the distance through which the solar system 
had moved in 75 years. His research, which was 
carried out with considerable mathematical refine<- 
ment, confirmed Herschel's earlier result. Many 
determinations of the solar motion have been made in 
comparatively recent years. The comparison of 
modern observations with the older ones of Bradley 
and others have given the proper motions of a large 
number of stars, so that bright stars and faint stars, 
stars of large and of small proper motions have been 
used in different determinations. Further, the diffi- 
culties and uncertainties of the problem have given 
rise to the development of somewhat different mathe- 
matical methods of treatment. The results were not 
as accordant as might have been anticipated, and in 
searching for the cause of the discrepancies Professor 
Kapteyn discovered an interesting feature in the 
proper motions arising from peculiarities in the 
motions of the stars themselves. The different 
methods by which the problem had been treated 
assumed that, apart from the apparent movements 
arising from the real movement of the §plar system 



DISTANCES AND MOVEMENTS OF STARS 185 

in space, the movements of the stars themselves were 
haphazard. It has been clearly demonstrated that this 
is not the case, but that the stars' movements exhibit 
a bias towards a direction whose right ascension is 
about 90 and declination about + 15° and the direction 
diametrically opposite. The point in the sky towards 
which the solar system is moving has right ascension 
275 and declination + 30 , and is not far from the 
bright star Vega. It is to be understood that there is 
an uncertainty of several degrees in the positions 
determined for both of these points. 

Motion in the Line of Sight. — The information derivable 
from the proper motions of stars has in recent years 
been supplemented by determinations of the actual 
velocities with which stars are moving to or from the 
Earth. The application of the spectroscope for this 
purpose was first made by Sir William Huggins in 
1868. The position of a line in the spectrum is deter- 
mined by the number of vibrations which are received 
each second. If the source of light is approaching the 
observer, more vibrations are received per second than 
is the normal case when the source of light is at rest. 
Suppose the spectrum contains known lines, for in- 
stance, those due to Iron. These will all be displaced 
slightly to the violet side of their positions in the 
normal spectrum of Iron; and the amount of the dis- 
placement affords a means of comparing the velocity 
of the source of light towards the observer with the 
yelocity of light. If the source of light is receding 



1 86 ASTRONOMY 

from the observer the lines are displaced towards the 
red. 

The initial difficulties of applying this principle to 
determine the velocities of the stars to or from the 
Earth were very considerable owing to the small 
amount of light from a star and also on account of 
the minuteness of the displacement. Sir William 
Huggins showed that the method was feasible, and 
Dr. Vogel, by substituting photographic for visual 
observations, substantially increased its accuracy. 
Later with the large telescope of the Lick Observ- 
atory, Prof. Campbell obtained still higher accuracy, 
and at the present time there are half-a-dozen observ- 
atories where the velocity of a bright star to or from 
the Earth can be obtained with a probable error of 
not more than half-a-mile a second. It is to be noted 
that, provided there is enough light for an observation 
to be made, the information we derive of the stars' 
velocities in this way is irrespective of their distance. 
As might be expected the velocities with which the 
stars are approaching or receding from the Earth 
vary considerably. Those with the greatest velocity 
determined at the Lick Observatory are — 

r} Cephei 55 miles per second towards Sun 

£ Herculis 45 ,, 

e Andromedae 53 ,, 

p Cassiopeiae 61 ,, 

8 Leporis 59 ,, ,, from Sun 

^Canis Majoris 59 ,, 



DISTANCES AND MOVEMENTS OF STARS 187 

From the velocities of 280 stars Prof. Campbell 
determined the direction and amount of the solar 
motion. The method is essentially the same as that 
employed in the case of proper motions. The 
velocity found for each star is supposed to be com- 
pounded of the velocity of the solar system and of 
the star itself, and from the manner in which stars 
at one part of the sky are systematically found to be 
moving towards the Sun, and in a diametrically 
opposite part of the sky to be moving from the Sun, 
the velocity with which the solar system is moving 
through space is found to be about 12J miles per 
second. 

Average Distances of Stars. — This velocity of 12J 
miles per second in a year carries the solar system for- 
ward a distance equal to 4a where a is the distance of 
the Earth from the Sun. In 100 years, therefore, the 
solar system moves a distance 400a, and the stars are 
seen from points 200 times as far apart as the extreme 
distance which the revolution of the Earth about the 
Sun supplies. 

Referring to the figure on p. 182, we may take O 
to be the position of the Sun in 1800 and O 7 in 1900. 
Let us suppose a number of stars at equal but un- 
known distances from the solar system to have had 
their positions in the sky observed in 1800 and again 
in 1900. From comparison of these observations the 
angle OAO 7 may be determined, and then as the 
length OO 7 is known, the distance OA of these stars 



1 88 ASTRONOMY 

can be found. As the stars are not all at the same 
distance, the application of this method in practice 
only gives the average distance of the stars considered. 
As an illustration, take the stars observed by Groom- 
bridge in 1810 and re-observed at Greenwich about 
1890. There were 200 stars brighter than 5*0 mag., 
454 between mags. 5*0 and 6'o, 1003 between mags. 
6'o and 7*0, 1239 between mags. 7*0 and 8*o, and 811 
between mags. 8*o and 9*0. Treating each group as if 
all the stars belonging to it were at the same distance 
from the solar system, the angle OAO ; or the paral- 
lactic angle was found to be 3' 17", 2*54", 2*28", 179", 
i"86 // for the several groups of stars. But in 80 
years the actual displacement of the solar system is 
320a, where a is the Sun's distance from the Earth, 
and thus the average parallaxes of these groups of 
stars are found by dividing the above angles by 320, 
and are therefore q'0099", o'ooSo", 0*007 i r/ , 0*0056", 
and o*oo58 /; . The distances corresponding to these 
parallactic angles are 20, 25, 30, 36 and 34 million 
times the distance of the Earth from the Sun. No 
stress is to be placed on these exact figures, which are 
only given to indicate roughly a method by which the 
distances of the stars may be approximately arrived at. 
Another method of obtaining an idea of the dis- 
tances of the stars is based on the very simple assump- 
tion that the density of the stars in space is the same 
at greater distances as it is near the Sun. If we take 
a sphere whose radius R is one million times the 



DISTANCES AND MOVEMENTS OF STARS 189 

Sun's distance, we know that there are 20 stars within 
this sphere, we should expect to find 20,000 stars 
within a sphere of radius 10R, and 20 million stars 
within a sphere of radius 100R. Precise results can- 
not be given till we are certain that all the stars 
are known which are within the smallest of these 
spheres. For this it will be necessary to wait till the 
results of the organized search for stars of large 
parallax have been obtained. The simple argument 
just given shows that while there are only a few stars 
nearer than a million times the Sun's distance, a very 
considerable number are within ten times the limit, 
and probably a large fraction of those visible to the 
naked eye are within a hundred times this limit. 

Only a very rough indication has been given of 
methods which may be applied with considerable 
detail. The brightness of a star, other things being- 
equal, is an indication of its distance. Similarly a 
star with large proper motion is probably nearer than 
one in the same part of the sky with a small proper 
motion. It has been established that the stars differ 
very much in intrinsic brightness, and thus the proper 
motion generally is a safer guide than the magnitude 
to the distance of a star. But magnitude and proper 
motion are not the only classifications which need 
to be considered in connection with stellar distances. 
As we shall see later the spectroscope enables stars 
to be classified according to their physical conditions. 
Most of the stars fall into one of two tvpes : those 



i go ASTRONOMY 

whose spectra exhibit broad lines due to hydrogen and 
sometimes to helium, such as Sirius, Vega and Rigel, 
and those whose spectra are, like the Sun, full of 
metallic lines, such as Capella and Arcturus. It is 
found that the yellow or solar stars are much nearer 
to us than the blue or Sirian stars. The following 
table by Kapteyn gives the mean parallaxes of stars 
of different magnitudes — 



Mag. 


Type I. 


Type II. 


2*0 


0*032" 


0*072" 


4 *o 


0*0 1 6" 


0*036" 


6*o 


0*008" 


0-018" 


8-o 


0*004" 


0*009" 


O'O 


0*002" 


0*0045 



The table shows that the mean distance is doubled 
as we pass from second to fourth magnitude stars, 
and so on; and that the mean distance of blue stars 
is more than twice that of yellow stars of the same 
magnitude. But it must be clearly understood that 
these are only average results, and that there are great 
differences in the distances of stars of the same 
magnitude. 

Velocities of the Stars. — It is beyond the scope of this 
book to go into the rather difficult statistical processes 
by which the average velocities of the stars are deter- 
mined. The following table by Professor New<comb 
gives in a simple form some of his conclusions. It 
should be remembered that a velocity of three miles 
a second would cover the distance from the Earth to 



DISTANCES AND MOVEMENTS OF STARS 191 



the Sun in one year. Taking 1000 stars, an estimate 
is made of the number of stars moving 3, 6, 9, etc., 
miles a second. 



Velocity 


No. of 


Velocity 


No. of 


Velocity 


No. of 


in miles 


Stars. 


in miles 


Stars. 


in miles 


Stars. 


per sec. 




per sec. 




per sec. 




O 


5 


27 


75 


54 


2 


3 


36 


30 


59 


57 




6 


66 


33 


44 


60 




9 


92 


36 


32 


66 




12 


107 


39 


22 


75 




15 


114 


42 


H 


90 




18 


1 12 


45 


9 


120 


1 


21 


103 


48 


6 


150 




24 


9 1 


5 1 


3 


180 





As the velocity of the Sun in space is about twelve 
miles per second, it is seen that the Sun's velocity is 
rather below the average of stellar velocities. 

Absolute luminosity of the Stars. — If the Sun and stars 
were all at equal distances from the Earth, how would 
their luminosities differ ? It is not easy to determine the 
ratio with accuracy, but we may take it that the light 
from the Sun is 40,000,000,000 times the light from the 
bright star Vega. Now, Vega is of magnitude o'i, 
and a little calculation from these figures shows that if 
the Sun were removed to two million times its dis- 
tance, when its parallax would beo'i ;/ , it would appear 
to us as a star of 5*1 mag., that is to say, would be just 
visible to the naked eye. As showing how much the 
stars vary in absolute luminosity the following table 



192 ASTRONOMY 

of Professor Kapteyn's may be quoted. In a space 
containing two million stars of the same luminosity as 
the Sun there are — 

i star with 100,000 times its luminosity. 

38 stars ,, 10,000 ,, ,, ,, 

1800 ,, ,, 1000 ,, „ ,, 

3600 ,, ,, 100 ,, ,, ,, 

440,000 ,, ,, 10 ,, ,, ,, 

5 million stars with T Vth of the Sun's luminosity. 

t1 - 1 -th 

/ 2 > > ' > " 100 1 " " > » ' > 

Naturally figures of this kind do not pretend to any 
great degree of exactitude; but the table given above 
is based on a careful discussion of such material as 
exists, and may be taken as an approximate statement 
of the great diversity which exists in the intrinsic 
brightness of the stars. 



CHAPTER IX 

STARS AXD NEBULA 

In the last chapter the questions to be answered 
were: Where are the stars? and How are they mov- 
ing? Another series of questions which naturally 
present themselves are concerned with their chemical 
and physical nature. What are the stars made of? 
What are their temperatures ? How far do they 
resemble the Sun and in what respects do they differ 
from it? Partial answers to these questions can be 
obtained from a study of stellar spectra, which teach 
us three distinct things, (i) By comparison with 
terrestrial spectra something is learned of the chemical 
composition of the stars. Hydrogen and helium, 
sodium and calcium, iron and titanium are perceived 
in stars ioo million million miles away. (2) By slight 
displacements of the spectral lines from their normal 
positions, movements in these distant bodies towards 
or from the Earth are detected and measured. (3; 
By the differences in character of the spectra, facts 
about the physical condition of the stars, such as their 
temperatures and the extent of the atmospheres sur- 
rounding them, may be gathered. These three lines 
of research are not entirely distinct, though they are 
o 193 



i 9 4 ASTRONOMY 

so to a large extent. The interpretation of the 
physical conditions which give rise to the peculiar- 
ities in stellar spectra is a matter of difficulty. This 
is not to be wondered at, for the spectrum of a sub- 
stance observed in a laboratory differs according to 
the temperature, pressure, and electrical conditions of 
the source from which the light is obtained. In the 
stars these conditions are varied far more than our 
means of experiment will permit. 

Stellar spectroscopy practically dates from 1863 with 
the researches of Sir William Huggins in England 
and Father Secchi in Rome. The very considerable 
difficulties to be overcome arise primarily from the 
limited quantity of light a star affords. Only a por- 
tion of this passes through the narrow T slit (say 
2170th inch wide) of a spectroscope; it is then spread 
out into a line of several inches in length from the red 
at one end to the violet at the other; and further, in 
order to see the structure of the line, it is necessary 
that it should be broadened into a narrow band by 
means of a cylindrical lens. When the light is spread 
out in this way its intensity is greatly diminished. 

The introduction of photography made a great 
advance in the accuracy and the range of stellar 
spectroscopy. Difficulties still arise, though in an- 
other form, from the small quantity of light which is 
submitted for analysis. Long exposures are necessary, 
and therefore the light of the star must be kept con- 
tinuously on the slit of the spectroscope. Further, 



STARS AND NEBULA 195 

the spectroscope must be so mounted that no flexure 
occurs in the different positions which it takes when 
the telescope follows the same star for several hours ; 
and again, arrangements have to be made to keep the 
temperature of the prisms constant (to within a small 
fraction of a degree), so that their density may not 
change and give a blurred picture of the spectrum. 

As the result of an examination of the spectra of 
more than 4000 stars, Secchi made an empirical classi- 
fication of the stars into four types. In the first type 
he included white and blue stars, such as Vega and 
Sirius, whose spectra show broad dark lines due to 
absorption of certain rays by hydrogen. The second 
type contained yellow stars, like the Sun, Capella and 
a Centauri, whose spectra show many fine metallic 
lines and two broad lines in the violet part of the 
spectrum due to calcium. The third type contained 
red stars, of which Antares is an example, whose 
spectra contain a number of dark bands, sharp on the 
violet side and fading off gradually to the red. The 
fourth type also consisted of red stars, whose spectra 
consist of dark bands due to the presence of carbon, 
sharp on the red side and fading off towards the 
violet. A fifth type was added later by Messrs. 
Wolf and Rayet of the Paris Observatory consisting 
of stars whose spectra contained dark bands and 
bright lines as well. 

In the Draper catalogue of the Harvard Observa- 
tory the spectra of more than 10,000 stars are classified 
o 2 



196 



ASTRONOMY 



by Mrs. Fleming. Still more recently, from an ex- 
amination of 4800 spectra of 681 stars taken with a 
larger telescope and greater dispersion, a careful and 
elaborate division of the stars into 22 groups has been 
made by Miss Maury. This subdivision into 22 
groups emphasizes the gradual change from type to 
type. The most important difference between this and 
Secchi's classification is the subdivision of the stars of 
Type I. 

All the stars of Secchi's first type are marked by 
the series of hydrogen lines which gradually close up 
to a point in the ultra-violet part of the spectrum. 
About 30 of these lines are seen ; they were discovered 
in the photographs taken by Sir W. Huggins. The 
wave-lengths were shown by Prof. Balmer to follow 
a very simple law — 



K = 3647*14 X , 



where n = 3, 4, 5, 6, and so on. 



The appearance of these broad -hydrogen lines in the 
spectra of certain stars is shown in Diagram 
LXXVIII. 



37 



38 



*2- 



1 * i > * 



uo 



Diag. LXXVIII. 



Helium Stars. — When helium was discovered in 1895 
by Sir W. Ramsay, it was found that some of these 
stars with broad hydrogen lines showed a large 



STARS AND NEBUL/E 197 

number of helium lines as well. The helium stars 
also contain lines due to oxygen, silicon and nitrogen. 
But lines due to metals are found in very few of them. 
Many of the bright stars of Orion belong to this 
class, Rigel and Bellatrix among them. Another 
helium star is /3 Crucis, in the Southern Cross — the 
first star in which the presence of oxygen was recog- 
nized (by Mr. McClean in 1897). 

Hydrogen Stars. — Sirius and Vega are the brightest 
of the hydrogen stars. In the spectra of this group 
the helium lines are not present. Between the broad 
lines of the hydrogen series a number of metallic 
lines are faintly shown in some of the stars. Thus in 
Sirius are seen lines due to sodium, calcium, mag- 
nesium, silicon, iron, titanium, vanadium. Oxygen 
and nitrogen are not shown. 

More than half the stars in the sky belong to 
Secchi's first type. A remarkable feature about them 
is their small proper motions, indicating that as a 
class they are very distant from the Sun. This is 
specially true of the helium stars. Many of these 
stars are, however, of very great brilliancy. Sirius, 
for example, gives us 20 times as much light as the 
Sun would if placed at the same distance, but is only 
between two and three times as massive as the Sun. 
This may result from great intrinsic brightness or 
very large surface. Again, the blueness of these 
stars may be taken as evidence that they are not sur- 
rounded by a dusky veil like the Sun. 



1 98 ASTRONOMY 

Solar Stars. — The most conspicuous stars of this type 
are Capella and Arcturus. Their spectra are almost 
exactly similar to that of the Sun. Procyon and 
Canopus are intermediate between the Sirian and solar 
stars, as they show the hydrogen series as well as 
strong metallic lines. A very large number of stars 
belong to this group. Some, like Arcturus, are at 
a very great distance, while a Centauri is very near. 
The similarity of their spectra to that of the Sun 
shows that these stars are of similar intrinsic bril- 
liancy. The great differences in their apparent 
brightness is therefore to be attributed solely to 
distance and actual size. Making allowance for 
distance, Arcturus is found to be many thousand 
times more bulky than the Sun, a Centauri to be 
nearly the same size, and some other stars much 
smaller. 

Stars of the Third Type. — When we come to stars of 
the third type, it is found that a larger proportion of 
their total light is in the red end of the spectrum — 
the blue light is absorbed as in solar stars, but to a 
greater extent. The bands, sharp at their violet edges 
and fading off towards the red, which are the charac- 
teristic feature of this type, have recently been shown 
by Prof. Fowler to be due to titanium oxide. The 
same bands have been found by Prof. Hale in Sun- 
spots. The general appearance of the bands is given 
in Diagram LXXIX. The existence of an oxide is 
taken as an indication of comparatively low tempera- 



STARS AND NEBULA 



199 



ture. Besides the bands, there are a great many lines 
due to metals. Antares and Betelgeux, the brightest 
stars belonging to this type, are at very great dis- 
tances, and appear to be very much greater than the 
Sun. 



.:-.:■■;■ 


fe M 


ft 


Ir ' 


^— 




% 

V 


•a 


1 3 a 3 a a 


i 5 $ 






Diag. LXXIX. 









Stars of the Fourth Type. — These are comparatively 
few, and none are brighter than the fifth magnitude. 
They are characterized by three bands sharp towards 
the red and fading away towards the violet, which 
were identified by Secchi as due to carbon com- 
pounds. The spectra of this group of stars have 
been carefully studied by Prof. Hale and Mr. Eller- 
man at the Yerkes Observatory. They are shown to 
contain, in addition to the bands, a large number 
of dark lines and a few bright ones. The presence 
of sodium and iron, among other bodies, is indicated 
by the absorption lines. 

Stars of the Fifth Type.— The Wolf-Rayet stars 
have complex spectra, consisting of the superposition 
of a continuous, bright line and a dark line spec- 
trum. Some of the lines are due to helium and 
hydrogen, but the rest are unidentified. There are 
no metallic lines. The brightest star of the class is 
y Argus. In it the first line of hydrogen is bright, 



200 



ASTRONOMY 



the second neutral, and the rest dark. A remarkable 
feature about these stars is the existence of a series 
of lines, whose wave-lengths can be derived from the 
formula for the hydrogen series on p. 196 by giving 
n the values 3J, 4J, 5J, etc. This points to the exist- 
ence of hydrogen under conditions which have not 
been obtained in any laboratory experiments. These 
Wolf-Rayet stars are all found in the neighbourhood 
of the Milky Way. 

In addition to these stars, Miss Maury has a class 
whose spectra are like the helium or Orion stars, but 
in which some of the lines are bright instead of dark. 

The following table, taken from the Harvard 
Annals, shows how the 681 brightest stars between 
the north pole and 30 S. declination are divided 
among the different classes — 

Helium 117 

Intermediate . . . . . 31 

Type I. Hydrogen .... 185 

Intermediate . 35 

Type II. Solar 218 

Type III. Titanium Oxide . . 55 

Type IV. Carbon .... 4 

Type V. Wolf-Rayet ... 4 

Helium stars with some bright lines . 14 

Composite spectra (probably binaries) 18 

The table shows that a very large percentage of the 
stars are included in the three types of helium, hydro- 
gen and solar stars. The same result is found when 
the classification is extended to include fainter stars. 



STARS AND NEBULAE 201 

Nebulae. — The relationship of these various classes 
of stars to one another cannot be understood without 
reference to an apparently very different kind of body. 
With his small telescope Halley found two nebulous 
patches of light in the constellations of Andromeda 
and Orion. Herschel with his great telescopes dis- 
covered thousands of faint nebulous areas. Some 
were irregular and diffuse, others nearly circular and 
small. He could not say certainly whether they 
consisted of faint stars crowded together, or were 
continuous bodies of luminous fluid. Most of the 
nebulas discovered by Herschel are faint and invisible 
except with large telescopes, so much so that the Bonn 
Durchmusterung, which contains more than 300,000 
stars visible in a small telescope, gives no more than 
64 nebulas. 

The key to the nature of these bodies was found by 
Sir William Huggins in 1864. Light from the bright- 
est of the nebulae, that of Orion, was collected by the 
object glass of a telescope, and a small part of it sent 
through the slit of his spectroscope to be analyzed. 
The spectrum was not a bright band with dark absorp- 
tion lines across it like the solar spectrum, but con- 
sisted simply of four bright lines, of which the bright- 
est was green. The nebula, therefore, was composed 
of glowing gas of low density. Other nebulae were 
found to contain the same lines, two of which were 
identified with hydrogen, and the brightest of all was 
at first thought to be due to nitrogen. Larger tele- 



202 ASTRONOMY 

scopes and spectroscopes of greater dispersion have 
since been employed, and show that this is not the 
case, and the origin of two of the lines is still un- 
known. An unknown element nebulium may give 
rise to them, or possibly some known element, but 
under conditions which have not yet been reproduced 
in our laboratories. A number of fainter lines have 
since been discovered in the spectra of nebulas, 
among others the yellow line due to helium identified 
by Prof. Copeland. The most extensive study of 
nebular spectra has been made at the Lick Observa- 
tory by Prof. Keeler, who succeeded in determining 
the velocities with which 14 were approaching or 
receding from the Earth, as well as the exact wave- 
length of nebular lines of unknown origin. 

Nebulae do not all show a spectrum consisting of 
bright lines. The Andromeda nebula and a very 
numerous class of spiral nebulae show a continuous 
spectrum. 

Our knowledge of nebulae has been largely increased 
by the beautiful photographs which have been taken 
in recent years. When a telescope is used with a 
high magnifying power only a very small area of the 
sky can be seen at one time. This is of no conse- 
quence if we are measuring a close double star or 
examining a planet, but with extended bodies like 
some of the nebulae it is a great advantage to have 
the whole object before the eye at one time in a 
photograph. Again, a photographic plate with a 



STARS AND NEBULA 203 

sufficiently long exposure receives impressions which 
make no perceptible effect on the retina, and thus 
faint nebulae and the faint details of bright nebulae 
are recorded which could not be observed visually. 
A third advantage is that the photograph itself is an 
unbiassed and permanent record of the observations. 

An English amateur astronomer, Dr. Common, 
succeeded in 1883 in obtaining a beautiful photograph 
of the great nebula in Orion. He used a large reflect- 
ing telescope of his own construction, which possessed 
great light-grasping power owing to its large size in 
proportion to its focal length. Following him, Dr. 
Roberts, another amateur, made an extensive series 
of photographs of nebulae, of which he published the 
most interesting and striking. Many photographs 
have since been taken at various observatories, either 
with reflectors or refractors of short focus. A beau- 
tiful series of photographs taken by Prof. Keeler 
at the Lick Observatory, including all the remarkable 
nebulae visible in that latitude, has recently been 
published. 

The nebula of Orion is perhaps the grandest object 
the telescope reveals to us. Its brightest part covers 
an area of the sky somewhat less than that covered 
by the Sun. It cannot be less than 10 million times 
the Sun's distance from us. The distance from one 
side of the nebula to the opposite side is not less than 
10 million million miles, or, comparing with the size 
of the solar system, 4000 times as large as the distance 



20 4 ASTRONOMY 

from the Sun to Neptune. The tenuity of the nebula 
must be of a far higher order than any vacua with 
which we are acquainted, otherwise the mass would 
produce very great velocities in the stars near it. 
Some of the stars seen with it appear to be physically 
connected with the nebula, and not to be merely in 
the line of vision. This applies especially to four 
stars forming a trapezium in its brightest part. It 
was found by Sir W. Huggins that the spectra of 
these stars contain a number of bright lines identical 
with some in the nebula. They may have been 
formed by the condensation of some of the gaseous 
matter. The displacement of lines in the spectrum 
shows the distance between the nebula and the Sun 
to be increasing at a rate of 10 or n miles a second. 
This apparent movement is nearly all due to the 
movement of the Sun in the opposite direction. 
There are indications of different velocities in different 
parts of the nebula, but these are not greater than 
one or two miles a second. Changes in the lumin- 
osity of parts have been suspected, but have not been 
certainly established. The source of this luminosity 
(which is excessively small compared with that of the 
Sun) is unexplained, but there is no reason to sup- 
pose that the nebula is at a high temperature. Dia- 
gram LXXX, from a photograph taken at Greenwich 
with a 30-inch reflector and an exposure of 2 h. 15 m., 
shows the general appearance of the nebula. 

The forms of nebulae have been much better under- 



STARS AND NEBUL/E 205 

stood since photographs have been obtained. Some 
are wholly irregular and diffuse, like that of Orion, 
but several are ring-formed, and a very large number 
are spiral. Prof. Keeler estimated that in the whole 
sky there were 120,000 nebulae of spiral form within 




Diag. LXXX. — Orion Nebula. 

easy reach of the light-grasping powers of the reflect- 
ing telescope of the Lick Observatory. 

Although the process is not fully understood, it 
seems probable that stars have been evolved from 
nebulae. The relationship of the stars in the Orion 
nebula to the nebula itself and the forms of spiral 
nebulae confirm the view that the long-continued 
action of gravitation converts the nebulae into stars 



206 ASTRONOMY 

and stellar systems. The bright line spectra of nebulse 
have therefore been taken as a starting-point in clas- 
sifying the stars according to their order of develop- 
ment. Classifications have been proposed by Huggins, 
Vogel, Lockyer, and McClean, which differ in some 
particulars, owing to the difficulty of interpreting 
spectra. The following is given by Prof. Hale as the 
one corresponding most closely with current views — 

Nebulae. 

Helium stars. 

Hydrogen stars. 

Solar stars. 

Titanium oxide and carbon stars. 

Dark stars. 

The Wolf-Rayet stars are probably in an early 
stage of development. 

We suppose, then, that a star begins as a nebulous 
mass. This condenses and forms helium stars, like 
those found in the centre of the Orion nebula. At 
first only helium and hydrogen are seen in the spectra, 
but gradually lines of oxygen, nitrogen, magnesium 
and silicon are found. Next we come to stars, like 
Sirius, in which the helium lines are not seen, but 
where there are broad hydrogen lines, supposed to be 
characteristic of very extensive atmospheres, as well as 
fine metallic lines. The study of variable stars shows 
that hydrogen stars are of much less density than the 
Sun. It is probable that so far the stars have been 
getting hotter, for more heat is obtained by contrac- 



STARS AND NEBULA 207 

tion than is lost by radiation, as long as a star remains 
gaseous. After the hydrogen stars, the order pro- 
ceeds through stars like Procyon to Capella and 
Arcturus, which resemble the Sun. The spectra of 
these yellow stars is marked by the number of metallic 
lines, the disappearance of all but the first five of the 
broad hydrogen lines, and the prominence of two 
calcium lines in the violet. Further, an absorbing 
atmosphere, like the dusky veil round the Sun, cuts 
off a large amount of the violet and blue light. Next 
we come to the red stars, in which the absorbing 
atmosphere has grown more intense and cuts off still 
more of the blue light. The presence of compounds 
with fluted spectra shows that these stars are of lower 
temperature than the solar stars, and are declining 
to the stage of dark stars. There are no doubt dif- 
ferences in the evolution of different stars. A large 
star will probably be longer in going through its 
stages than a small one. Of the length of time occu- 
pied we have no idea. 



CHAPTER X 

DOUBLE STARS AND CLUSTERS 

Sir William Herschel is generally spoken of as 
the founder of Sidereal Astronomy. He took for 
his motto " Whatever shines should be observed, " 
and constructed telescopes far surpassing in light- 
grasping and penetrating power those of his pre- 
decessors, with which he executed a most thorough 
and minute exploration of the sky. Herschel was, in 
addition, a philosopher who interpreted what he saw 
with the consistent aim of obtaining as completely 
as possible a rational description of the sidereal uni- 
verse, but it is to his persistence and enterprise as an 
explorer of the skies that the discovery of double stars 
is due. 

While making an examination of the sky for the 
purpose of finding some stars of measurable parallax, 
he discovered that many stars were double, and in 
1782 presented to the Royal Society a catalogue of 269 
double stars. He supposed at the time that these 
were only optically double, that is, were nearly in the 
same line as seen from the Earth. His intention was 
doubtless to see if in any cases a movement of the 
brighter star relative to the fainter, such as would 

arise from their different distances, could be discerned 

208 



DOUBLE STARS AND CLUSTERS 



209 




in the course of the year. He was, in fact, seeking 
to determine the parallax of a star, in the way which 
was successfully carried out by Bessel in 1831, and 
which is described in Chapter VIII. 

The observation of a double star will be understood 
from Diagram LXXXI . If A and B are the two stars, the 
distance AB between them 
is measured, and also the 
angle BAN, between the 
line joining the stars and 
the meridian through the 
star A. By 1803 Herschel 
had sufficient evidence that 
some of the stars he had 
observed were not double 
in appearance only, but 

were real binary combinations of two stars, 
together by the bond of mutual attraction, 
bright star Castor first convinced Herschel of the 
existence of double stars with orbital motion about 
one another. In the space of 22 years the direction of 
the line joining the stars had changed by more than 
20°. (Castor is easily seen to be double with a small 
telescope; the distance between these two stars is 
about 5" ; both are bright, one being of mag. 2*7 and 
the other 3*7.) Herschel concluded that the stars 
revolve round one another in 342 years. Similarly 
he found for y Leonis a period of 1200 years, for 6 
Serpentis 375 years, for e Bootis 1681, and for y 
p 



Diag. LXXXI. 



held 
The 



2io ASTRONOMY 

Virginis 708 years. He also found that e Lyrae is a 
double double star. Herschers work was continued 
by his son, and by Sir John South, but most of all by 
Wilhelm Struve at Dorpat. Struve made measures 
of all stars he knew to be double, and in addition 
made a minute review of the heavens from the north 
pole to 15° south of the equator. He examined 
120,000 stars, and produced a great catalogue con- 
taining 2640 double stars. Since Struve's time the 
number of astronomers who have given attention to 
the observation of double stars is considerable, and 
has included some of exceptionally keen eyesight. 
With the assistance of larger telescopes the scrutiny 
of the stars has been pushed further, so that very faint 
companions to bright stars have been discovered, and 
many which with small telescopes appear to be single, 
have been resolved into very close double stars. 
Especially conspicuous is the work of Prof. Burnham 
at various observatories in the United States, and of 
his successors, Profs. Hussey and Aitken, at the Lick 
Observatory. 

During the time they have been under observation, 
some double stars have made a complete revolution 
about one another, and in many cases sufficient move- 
ment has taken place for an accurate determination 
of the period or time of revolution. The shortest 
period as yet found is about 5J years. There are a 
considerable number whose periods are between 20 and 
50 years, and a great many whose periods are hundreds 



DOUBLE STARS AND CLUSTERS 



211 



of years. The orbit of £ Bootis, shown in Diagram 
LXXXII and taken from a work by Mr. T. Lewis on 



£3ooris 




Diag. LXXXII. 

the double stars observed by W. Struve, may be con- 
sidered as that of a typical double star whose compo- 
nents are fairly widely separated. The brighter star of 
p 2 



212 ASTRONOMY 

the pair at A is of magnitude 47, and of yellow colour ; 
the companion is of magnitude 6*6, and is purple. 
The relative positions of the stars as seen by Herschel 
in 1780 and 1802, by Struve in 1822, and subsequent 
observers, are indicated by dots. These dots all lie on 
an ellipse, but it is not an ellipse with A as focus, 
for we see not the true orbit of the star about its 
primary, but the projected orbit on a plane perpen- 
dicular to the line joining the Earth and the star. 
The true orbit may be determined from the apparent 
one by calculation. In the case of f Bootis the com- 
plete revolution will be accomplished in about 137 
years. The length of the major axis of the apparent 
orbit is g'60", and of the minor axis 5*6i // , and cal- 
culation shows that the major axis of the true orbit is 
io*66 /; , the minor axis 8'53 // , and that the true orbit 
is inclined at an angle of about 50 to the apparent 
orbit. 

When the distance of a double star from the Earth 
is known, it is possible to determine the actual dis- 
tance between the stars. Take, for example, the bright 
star Sirius, which has a very faint companion. The 
parallax of Sirius is known to be 0*37", and the semi- 
major axis of the orbit of the companion around Sirius 
is approximately 8'o r/ . Construct a diagram (Dia- 
gram LXXXIII) in which © stands for the Sun and 
S for Sirius, and let ©S denote the distance of the 
Sun from Sirius. Draw ©E perpendicular to ©S, 
and make ©E equal to the Earth's distance from the 



DOUBLE STARS AND CLUSTERS 



213 



Sun on this scale. Similarly let SS 7 denote the semi- 
major axis of the orbit of the companion about Sirius 
on the same scale. Then 




Diag. LXXXIII. 



the angle ESQ = parallax of Sirius = 0'37"\ 
and the angle SQS' = semi-major of orbit = 8'0." J 

From which it follows that SS' : QE = 8'o" : 0-37", 

or that the semi-major axis of the orbit is — , or 22 
J '37 

times the Earth's distance from the Sun. Thus the 
linear dimensions of the orbit of the faint companion 
around Sirius are known. 

Further, the combined mass of the bright star and 
its companion can be compared with that of the Sun. 
The attraction of the Sun causes the Earth to make 
its revolution in one year. The companion of Sirius 
takes 50 years to go round Sirius, and its mean dis- 
tance from Sirius is 22 times that of the Earth from 
the Sun. As we have seen in Chapter III (p. 52), 
we can from these data find the sum of the masses of 
Sirius and its companion. Calling them m and ra', 



2i 4 ASTRONOMY 

and that of the Sun M, we have the equation 

m + rri /22\ 3 / i \ 2 ' 

— yr — vl/ ' vso/ = 4'3, or the sum of the masses is 

4*3 times that of the Sun. 

In the case of Sirius and a number of other double 
stars it is possible to compare the masses of the 
primary star and of its companion. This, however, 
requires other observations than the relative move- 
ments of companion and primary afforded by double 
star measurements. In these measures the companion 
is considered as describing an ellipse about its prim- 
ary, whereas both the primary star and companion are 
describing ellipses about their common centre of 
gravity. Before the companion of Sirius was dis- 
covered it was known to exist, because Sirius was seen 
to have a slightly irregular movement in the sky. In 
addition to its proper motion in a straight line, it was 
seen to be describing a small ellipse in 50 years. In 
1844 Bessel was convinced that the explanation of this 
elliptic movement of Sirius was to be attributed to an 
invisible but massive companion. In 1862 Mr. Alvan 
G. Clark, while testing an object glass of 18 inches 
aperture by examining the appearance of Sirius with 
it, discovered this faint companion. It was only of 
the tenth magnitude, and thus 16,000 times fainter 
than Sirius, and at the time of discovery was io /; 
distant. When the meridian observations which had 
indicated the movement of Sirius about its centre of 
gravity were investigated in 1864 by Dr. Auwers, it 



DOUBLE STARS AND CLUSTERS 215 

was found that the bright star described an ellipse 
whose semi-major axis was 2'ss" '. Thus in Diagram 

LXXXIV, where S 1 1— .^ 

is Sinus, S the M T 

Diag. LXXXIV. 

faint companion, 

and G the centre of gravity, SG = 2"33 /; and SS r = 
8*00", and therefore S r G = 5*67". The mass of the 
faint companion is therefore greater than that of 
Sirius in the proportion of 5*67* to 2'33 /; , or about 
2 J to 1. Taking the total mass to be 4*3 times that of 
the Sun, we see that Sirius itself is about i"2 times the 
mass of the Sun, and the dark, almost invisible, com- 
panion is rather more than 3 times. In other cases 
where it has been possible to compare the bright and 
faint components of a double star, the faint component 
has usually been found to be the more massive. 

Spectroscopic Binaries. — Sirius and Procyon were 
shown to have invisible companions from their vari- 
able motion on the face of the sky. In a large number of 
cases stars which are apparently single have been shown 
to be double by variations disclosed by the spectro- 
scope in the velocity of the star to or from the Earth. 
Let us consider the simplest case. Suppose there are 
two stars, S and s (Diagram LXXXV), which are 
describing circles about their centre of gravity, G, and 
suppose the Earth to be in the same plane as their 
orbit in the direction GE, but so far away that the 
stars appear single in the largest telescope. When 
the star S is at S 1 , S 2 , S 3 , S 4 , the companion will be 



2l6 



ASTRONOMY 



at s^ s 2 y $ 
through G. 



*> 



s 4 , so that the line Ss always passes 
Further, for simplicity, let us suppose 
that G is at rest relative to 
the Earth. When the star 
S is at Sjl it is moving 
away from the Earth, and 
the lines of its spectrum 
will be shifted from their 
normal position towards the 
red end of the spectrum, 
and from the amount of this 
shift the velocity of S can 
be determined. At the same 
time the star s is at s v 
and moving towards the 
Earth, the lines of its spec- 
trum will be shifted towards the violet from their 
normal positions by an amount which measures the 
velocity of 5. When S is at S 3 , and 5 is at s 3 the con- 
ditions will be reversed. At the intermediate points 
when S is at S 2 or S 4 , and s at s 2 or s 4 , the stars 
have no velocity to or from the Earth, and the lines 
in their spectra will not be displaced from their normal 
positions. 

When the spectrum of a binary star which is seen 
single in the telescope is photographed, the result is 
the same as if the spectra of two separate stars 
had been photographed on the same plate. It may 
happen that S is a bright star and s a very faint one, 




DOUBLE STARS AND CLUSTERS 217 

in which case the spectrum of s will not he recorded. 
Again, it is possible that S and 5 may be two stars 
of nearly equal magnitude and similar spectra, in 
which case, owing to the shift of the lines due to the 
motion of the stars, lines in the spectra will sometimes 
appear doubled. A third possibility is that S may be a 
star giving an entirely different spectrum from s, in 
which case two separate spectra are superposed. But 
in all cases photographs of the spectrum of a binary 
star, taken when the components are in different rela- 
tive -positions, will show displacements of the lines 
due to the varying velocities of the stars in the direc- 
tion of the Earth. 

A large number of stars have proved to be spec- 
troscopic binaries. Some have been discovered from 
the composite character of their spectra, w 7 hich 
looked like the spectra of stars of two different types 
on the same photograph. Others have been dis- 
covered in the course of measurements of the positions 
of lines in spectra made with the intention of deter- 
mining the velocity of the star to or from the Earth. 
The spectra obtained on ditferent days have given 
different results, and subsequent photographs have 
shown the changes to be regular, and such as can be 
accounted for by supposing the stars to be binaries. 

The spectrum of Mizar (( Ursae Majoris), a bright 
star of the Great Bear, was found by Miss Maury to 
have the K line (due to calcium) double on two photo- 
graphs taken at Harvard in 1887 an d 1889, but 



218 ASTRONOMY 

single on other photographs. Examination of 72 
photographs showed that the changes in the spectrum 
occur at regular intervals, and were explicable if 
Mizar consists of two stars which revolve round one 
another in 104 days. Further, the relative velocity 
of the two stars was found to be about 100 miles per 
second. Assuming them to be of equal mass, and 
that the plane in which they move passes through 
the Earth, the two components are 140 million miles 
apart, and their combined mass is 40 times that of 
the Sun. 

In 1890 Vogel found that Spica was a spectroscopic 
binary. In this case the star consists of the bright 
star we see and a dull but massive companion. The 
displacements of the lines in its spectrum from their 
normal positions are completely explained on the 
assumption that Spica revolves about its companion 
in 4 days approximately with a velocity of 57 miles 
a second if the plane of the orbit passes through the 
Earth. If the orbit is inclined to the direction joining 
the Earth and star, as it is certain to be to a greater or 
less extent, the velocity will be greater than 57 miles a 
second, as the spectroscope only appreciates that part 
of a star's velocity which is directed to or from it. 

Another interesting spectroscopic binary is Capella. 
In 1 goo Prof. Campbell at the Lick Observatory, and 
Prof. Newall at Cambridge, independently found that 
Capella consists of two stars, one like the Sun in 
type of spectrum, and the other like Procyon. These 



DOUBLE STARS AND CLUSTERS 



219 



two stars revolve about one another in a period of 
104 days. 

The following example, a Carinae, discovered by 
Mr. Wright in the course of a Lick Observatory ex- 
pedition to the southern hemisphere, is a fairly typical 
case. From photographs of the spectrum of this star 
on 25 nights the following velocities were found in 
kilometers per sec. (1 km. = | mile) — 



Date. 


Vel. 


Date. 


Vel. 


1904 Feb. 


29.67 


+ 57 


1907 Feb. 


6.67 


+ 2*0 


1905 Jan. 


30.68 


+ 33' 2 




19-73 


+ I -9 


Feb. 


9.64 


+ io*o 


Mar. 


2.74 


+ 4i'3 


Feb. 


22.62 


+ 4*6 




4-74 


+ 167 


Mar. 


7.58 


- I '2 




14.63 


+ 257 


1906 Mar. 


30.58 


+ 3'° 




16.63 


+ 44'3 


1907 Jan. 


J5-79 


+ 39'o 




J 9-S7 


+ 5-2 




19.81 


+ 3 1 " 1 




23-53 


+ 40-8 




21.76 


+ 44-4 




24.58 


+ 28S 




25.81 


+ 18-6 


Apr. 


3<M9 


+ 20-4 




26.79 


+ 3 1 ' 2 


May 


1.49 


+ 35*2 


Feb. 


2-75 
5-77 


+ 31-8 

+ l6"2 




11.48 


+ 57 



From these figures the period during which these 
fluctuations occur is found to be 6744 days; the velo- 
city of the centre of gravity of the system away from 
the Sun is 4- 23*3 km. per sec; and the velocity of 
the bright component of the star varies from o to 
+ 43 km. per sec. 

In the last few r years a very large number of spec- 
troscopic binaries have been discovered, especially 
with the large telescopes of the Lick and Yerkes 
Observatories, with their spectroscopes of great re- 



220 ASTRONOMY 

solving powers. In 1898 thirteen spectroscopic bi- 
naries were known. The number discovered to the 
end of 1905 was 140, and since that date the number 
has been nearly doubled. Prof. Campbell found one 
star in seven of those studied at the Lick Observatory 
to be a spectroscopic binary. The larger proportion 
of one in three was found by Prof. Frost at the Yerkes 
Observatory in the particular class of stars he was 
studying. In most cases the spectrum of only one 
component is visible, so that these binary stars, like 
Sirius consist of a bright star with a dull but massive 
companion. 

Clusters. — It has frequently happened in the course 
of double star observations that one of the two com- 
ponents has itself been found to be double. For 
example, y Andromeda was found by Herschel to 
consist of two stars of magnitudes 2*5 and 5*5 about 
io /; distant. Otto Struve found that the fainter com- 
ponent, when examined with a very large telescope, 
was itself a very close double star. In this way we 
have become acquainted with systems consisting of 
3 or 4 stars. But the sky contains groups of stars 
on a much grander scale. The Pleiades are one of 
the most familiar examples. In this collection of 
stars six are bright enough to be seen by most 
people with the naked eye, and six or seven more 
are visible to persons of specially keen sight, while 
a great many more are shown by an opera glass or 
small telescope. It is found that the brighter stars 



DOUBLE STARS AND CLUSTERS 



221 



among the Pleiades, and many of the fainter ones, 
have the same proper motion of 7 /; a century. They 
therefore form a group of stars moving together in 
space, and are not a mere optical group because they 
happen to lie nearly in line as seen from the Earth. 
The brighter stars have similar spectra, and the whole 
group is found by photographs taken with long 
exposures to be involved in a faint nebula. 

In Sir John Herschel's catalogue of nebulae in 1864 
he includes no globular clusters of stars. In these 
clusters the stars are 
seen much nearer to- 
gether than in the 
Pleiades. With a 
small telescope they 
cannot always be 
separated, and the 
cluster might be 
taken for a nebula ; 
but with a larger 
telescope they are 
resolved into separ- 
ate stars. Diagram 
LXXXVI, from a 
photograph with the 
great refractor of the 
Yerkes Observatory, taken by Prof. Ritchey, shows 
the appearance of the cluster in Pegasus. The stars 
are small and concentrated in the centre. The num- 




Diag. LXXXVI.— Cluster of Stars. 



222 ASTRONOMY 

ber of stars in some of these clusters have been 
counted. In a photograph of the southern cluster 
round <o Centauri, Prof. Bailey found more than 5000 
stars in a small area occupying about as much space 
as the Sun or Moon in the sky. Till we know the 
distance of the cluster it is impossible to say how far 
the stars in it are apart. 

A curious feature about the globular clusters of 
stars is the large percentage of short period variables 
(see Chapter XI). Thus in the cluster illustrated 
above out of 500 stars 91 are variable. 

In 1908 Prof. Boss pointed out that about 40 bright 
stars in and near the constellation Taurus form a 
small globular cluster, which is sufficiently near for us 
to see inside, so to speak, and learn its dimensions. 
Investigations of proper motions prove that these 40 
bright stars, of magnitudes 4*0 to 6*5, are moving 
towards one point in the sky. Diagram LXXXVII 
shows the direction of motion, the length of the 
arrows indicating the angular distance travelled in 
50,000 years. Apparent motion towards one point 
in the sky results from parallelism in the actual 
paths of the stars. The amount of proper motion, 
that is, projected angular motion on the face of the 
sky, is known for each star, and for three of them 
the velocity in the line of sight is also known. These 
facts are sufficient to show that these 40 stars 
are all moving in parallel directions towards a 
point RA 6b. 52m.; Dec. +7 with a velocity of 



DOUBLE STARS AND CLUSTERS 



28J miles a second 



and to determine the distance 
of each star from the Earth. The stars form a 
cluster of roughly globular shape. The centre of 















S/3 


r'-, 


5/r 


eai 


77 / 


nL 


?ur 


VS 








































——? 


^ 


r^ 








— +Zf 






























—^H 










— + /$ 


























- 




y™ 






■ ' '1 


ss— "= 






























^^ 


fe 


^ 








— ♦rs 




























z. r 












— -/J 
















- 
























*" 










'' - 


'*' 




-— 




























1 & 


if: 


'-;-■: 


\'S. 


' --- 


---- 


-- 


















- 
































— 


-— 


- 










— *S 



Diag. LXXXVII. 

the cluster has a parallax of about o , 025 // , correspond- 
ing to a distance of about 8 million times the Sun's 
distance. The distance of outlying stars in the cluster 
from one another is about 2 million times this dis- 
tance, so that the cluster is packed about as loosely 
as the Sun and its nearest stellar neighbours. The 
cluster was nearest to the Sun about 800,000 years 
ago, when it was at half its present distance. It is 
moving rapidly away, and will gradually assume 
the more compact appearance of a globular cluster, 
which in 65 million years will be only 20 ; in diameter, 
and consist of stars of 9th to 12th magnitude. Be- 
sides these 40 stars, 50 fainter stars of magnitudes 



224 ASTRONOMY 

6*i to 7*5 probably belong to the cluster, and doubt- 
less some still fainter ones will be discovered. To 
confirm Prof. Boss's results, the velocities in the 
line of sight of more stars in the cluster are being 
determined at the Yerkes Observatory. The curious 
fact has appeared that the stars are of Secchi's first 
type (hydrogen) and that 8 out of the 14 examined 
have proved to be spectroscopic binaries. 



CHAPTER XI 

VARIABLE STARS AND NEW STARS 

Variable Stars. — The discovery was made in 1596 
by Fabricius that the star o Ceti varies in brightness. 
Sometimes this star is easily visible to the naked eye, 
but at other times it is as faint as the eighth or ninth 
magnitude, and can only be seen with a telescope. 
Other variable stars were gradually discovered, and 
in 1844 Argelander published a catalogue giving 
particulars of the 18 stars which were then known to be 
variable and urged the importance of studying these 
bodies in detail. A great deal of attention has been 
given to variables since this date, and in recent times 
the information acquired by studying the variation of 
their light has been supplemented by that afforded by 
the spectroscope. The number of stars known to be 
variable has increased greatly, and in 1907 Prof. 
Pickering of Harvard published a catalogue of 3748 
of these bodies. He divides variable stars into five 
classes, and though the distinction between them is 
not absolute, this subdivision is rendered necessary 
by the well-marked differences between them. 

Eclipsing Stars.— Algol or j3 Persei is the best known 

type of this class. Its changes of brightness are 
Q 225 



226 



ASTRONOMY 



a c o to o 






regular and are repeated after a period of 2 days 20 
hours 49 minutes. 

For 2\ days the brightness of the star remains 
constant (2*3 mag.); in 4J hours it falls to 3*5 mag., 
and in the next 4 J 
hours returns to 2*3 
mag. When at its 
faintest Algol shines 
with only one third of 
the light it has in its 
brightest phase. These variations in magnitude are 
shown graphically in Diagram LXXXVIII, from 
which the magnitude at any time between January 
3 d. 3 h. and January 5 d. 25 h., 1910, may be inferred. 



¥ 



V~ 



Diag. LXXXVIII. 
Light changes of Algol. 





Diag. LXXXIX. 

Goodricke, who discovered the law of change in the 
brightness of Algol, suggested that the star possesses 
a dark companion, which periodically intervenes be- 
tween Algol and the Earth and cuts off a part of the 
light. Diagrams LXXXIX and XC illustrate exactly 
how this occurs. In Diagram LXXXIX the observer 



VARIABLE STARS AND NEW STARS 227 

is nearly in the plane of the orbital motion of the two 
stars, as is really the case, while Diagram XC shows 
the plan of the orbit. A is the bright star; B, C, D, 
E, F, are the dark star in different positions. When 
the dark star is at B, C or D part of the light from 
A is intercepted. 

In 1889 Prof. Vogel examined Algol spectroscopic- 
ally, and completely established the fact that the varia- 
tion of light is caused by a dark eclipsing satellite. 
If the bright star Algol has a dark companion they 
will revolve about their common centre of gravity. 
After the dark star has passed in front it will be 
moving away from the Earth and the bright star 
towards the Earth, and the maximum velocity will be, 
if the orbit is circular, one quarter of the entire period 
of revolution, or 17 hours after the epochs of 
minimum brightness. Similarly the maximum velo- 
city of the bright star from the Earth should occur 
17 hours before the epochs of minimum bright- 
ness. The spectroscope confirmed these surmises, 
and showed that 17 hours before mid-eclipse Algol 
is moving towards the Sun with a velocity of 39 
kilometres per second, and 17 hours after mid-eclipse 
from the Sun with velocity 47 kilometres per second. 
These figures show that Algol and its companion are 

moving from the Sun with a velocity of "^— ^or 4 

kilometres per second, and the velocity of Algol in its 

orbit is ^— or 43 kilometres per second, and, as 

Q 2 



228 ASTRONOMY 

we have seen, the time of describing the orbit is 2 days 
20 hours 49 minutes. 

From the loss of light experienced at mid-eclipse, 
the ratio of the diameters of the bright and dark stars 
may be inferred. From the ratio of the period of the 
eclipse to the period of revolution, the sum of the 
radii of the stars can be compared with the distance 
between their centres. Since the bright star is moving 
43 kilometres or 28 miles a second and takes 2 days 
20 hours 49 minutes, or nearly 250,000 seconds, to 
complete its circle about the centre of gravity of the 
two bodies, the radius of this circle will be rather more 
than one million miles. It is necessary now to make 
some assumption about the relative masses of these 
two stars, and Vogel, taking them to be of equal 
density, concludes that Algol is one million miles in 
diameter or 1*2 times the size of the Sun, the com- 
panion 800,000 miles, or about the size of the Sun, and 
that the distance between the centres is 3,200,000 miles. 

Between 30 and 40 variable stars resemble Algol. 
The period of variation is generally short, less than 
5 or 6 days, and the time of eclipse lasts for some 
hours. The bright and dark star are very close together 
in comparison with their diameters, as would naturally 
be expected, for otherwise the chance of the Earth 
being near enough to the plane of the orbit to witness 
eclipses would be very small. A remarkable feature 
in all these stars is their small mean density. In the 
case of Algol, for example, this is not more than I 
of the density of water. 



VARIABLE STARS AND NEW STARS 229 



Short-period Variables. — The characteristic of the 
variables whose periodic changes of brilliancy can be 
explained by the revolution of a bright and dark star 
around one another is the maintenance of the maxi- 
mum brightness for a large part of the whole period. 
The stars belonging to the second class change their 
light continuously. Sometimes in a complete period 
there are two maxima and two minima, sometimes 
only one. The changes of brightness generally occur 
in a space of less than 10 days and very rarely take 
more than one month. At least 60 or 70 variables are 
known to belong to this class. The three stars /? Lyras, 
5 Cephei and ( Geminorum may be taken as examples. 
/3 Lyrae goes through its changes in 12*9 days, having 
two maxima of magnitude 3*4, a primary minimum of 
magnitude 4*2, and a secondary one of magnitude 3*9. 
Its four phases of increasing and decreasing bright- 
ness are approximately equal. The variability of the 
star has been known since 
is difficult to interpret 
owing to the juxtaposi- 
tion of bright and dark 
lines and also on account 
of its variability. The 
changes which the spec- 
trum undergoes have the 
same period as the light-variation. Some of these 
changes are explicable on the hypothesis that 
two stars are revolving round each other. From 
a very elaborate investigation of the variation of 



1784. The spectrum 




Diag. XCI. 
Light changes of fi Lyrse. 



23° 



ASTRONOMY 



magnitude and changes in the position of certain lines 
in the spectrum observed by Prof. Belopolsky and Sir 
N. Lockyer, Prof. Myers of Indiana has deduced that 
the star consists of two large gaseous bodies very near 
together which revolve round one another. They are 
not quite spherical but owing to mutual gravitation 
are spheroidal. The smaller is 2\ times as bright 
as the larger and half as massive. The distance 
between their centres is 50 million miles, and the orbit 
they describe about one another is nearly circular. 
As the Earth is nearly in the plane of the orbit, in 
the course of a revolution first one body and then 
the other is partly hidden and the dimensions given 
are such as will account numerically for the changes 
of brightness. The spectroscope shows the stars to 
be gaseous, but Prof. Myers' figures give the astound- 
ing result that the mean density of the system is a little 
less than that of air. 

8 Cephei. — The light curve of h Cephei is very 

typical of short-period 
variables. The period 
of the light changes is 5 
days 8 hours 47 minutes 
40 seconds, but the time 
taken for the brightness 
to rise from the mini- 
mum to the maximum 
is much shorter than for 
In 1894 ^is star was shown by Belopolsky 




Diag. XCII. 
Light changes of 5 Cephei, 



the fall. 



VARIABLE STARS AND NEW STARS 231 



to be a spectroscopic binary, whose changes in velocity 
had the same period as the light changes. The 
spectrum of only one component is shown. The star 
is found to be moving in a very eccentric orbit, and if 
it exhibited no variation of light would be set down 
as a spectroscopic binary consisting of a bright and 
dark star. But the changes of light cannot be ac- 
counted for in this way, for it is found that the 
minimum brightness occurs a day before the time 
when the two stars are in line as seen from the Earth. 
The light variation cannot, therefore, be explained as 
due to an occultation of one star by another, and no 
satisfactory explanation has been given. 

C Geminorum. — This star goes through its phases 
in 10 days 3 hours 41 minutes 30 seconds. At its mini- 
mum the magni- 
tude is 4*5 and 
at maximum 37. 
The time during 
which the bright- 
ness increases is 
almost equal to 
the time during 




Diag. XCIII. 
Light changes of ( Geminorum. 



which it decreases. Forty-four 
photographs of the star's spectrum were taken at 
the Lick Observatory between November 11, 1898 
and February 11, 1900. These showed that the star is 
a spectroscopic binary, of which one component is 
bright and the other dark. The changes of velocity 
occur in the same period as the light changes. 



2 3 2 ASTRONOMY 

From the measures of velocity the orbit of the star 
was determined, but as in the case of 8 Cephei the 
time when the two stars are in line as seen from the 
Earth does not coincide with the time when the bright- 
ness is a minimum. The light variation does not 
therefore result from an eclipse. Some peculiarities 
in the velocities derived from the spectra suggest that 
as the dark and bright body are very close together, 
large tidal effects may be produced in the atmosphere 
of the bright star, and that the explanation of the light 
changes is to be looked for in causes of this nature. 

In the variables of short period it is clear that we 
are dealing with bodies of large size and small density. 
There can be no doubt of their essentially binary 
character. The two components appear to be very 
close together and may in some cases be joined by a 
neck. Possibly these variables present to us different 
stages in the segmentation of nebulous matter which 
is forming into two stars, the Algol class showing a 
further stage of this development. Such a view is, 
however, extremely speculative, as very little is known 
of the dynamical conditions to which such nebulous 
matter would be subject. 

Long-period Variables. — When a star is variable in 
a short period of less than a month, we have seen 
that the explanation is probably to be looked for in 
the rotation of two very close bodies. There are a 
large number of stars whose period of variability is 
much longer. More than 300 are known whose 



VARIABLE STARS AND NEW STARS 233 

periods lie between 200 and 400 days, and a con- 
siderable number beyond these limits. These are all 
classified as variables of long period. The difference 
in magnitude between these stars at their brightest 
and faintest is often very great — a difference of 5 
magnitudes or a variation of light in the proportion 
of 100 to 1 being not at all unusual. Generally speak- 
ing, the longer the period the greater the difference 
between the extreme magnitudes. These stars do not 
go through their variations with the same regularity 
as the variables of short period. The brightness at 
maximum varies from time to time, and the length 
of the period is not exactly the same from each maxi- 
mum to the next. Many of these stars are red or 
reddish. 

The most famous star of this class is Ceti, or Mira 
Ceti as it was called by Hevelius. In about S3 2 
days it increases in brightness from below the ninth 
magnitude to about the second and then diminishes 
again. Its variations have been watched for 200 
cycles, and its period has been seen to vary from 320 
to 370 days, but no law has been discovered for these 
changes. The greatest brightness the star attains also 
varies considerably. In 1779 Herschel saw it rise to 
magnitude 1*2; in 1868 it was only of magnitude 5'6 
at maximum; in 1897 lt reached the third and in 1905 
the second magnitude. Similarly its brightness at 
minimum has varied from 8'o mag. to 9*5 mag. 

The spectrum of Mira Ceti has been studied bv 



234 ASTRONOMY 

many astronomers. It consists of bright lines and 
dark bands. The dark bands are those found in stars 
of Secchi's third type, due to titanium oxide, while the 
bright line spectrum contains lines due to hydrogen 
and some metallic lines. The relative intensities of 
the bright lines vary in different parts of the star's 
cycle. There are no changes in the spectrum that 
suggest orbital motion. It would seem that there are 
periodically great outbursts of incandescence in the 
star itself. The changes which occur in long-period 
variables bear a resemblance to the periodic changes 
in the amount of the Sun's area covered with spots. 
The sun-spot period is long — about u years — and 
irregular. Sun-spot and long-period variables show 
the banded spectrum of titanium oxide. These sug- 
gest that long-period variables may be stars which are 
periodically largely covered by spots. 

New Stars. — Passing over another group of variable 
stars in which the light fluctuates in an altogether 
irregular manner we come to a very remarkable class 
which bear some resemblance to variables of long 
period. These are the new stars. Hipparchus, Tycho 
Brahe, and Kepler all witnessed with astonishment 
the appearance of new stars in the sky. Two were seen 
in the seventeenth century, and eight in the nineteenth, 
while in this century two have been found, one by Dr. 
Anderson at Edinburgh, and one photographically by 
Prof. Turner at Oxford. The new stars from which 
most has been learned are Nova Aurigas of 1892 and 



VARIABLE STARS AND NEW STARS 235 

Nova Persei of 1901, both of which were discovered 
with the naked eye by the same amateur astronomer, 
Dr. Anderson. Nova Persei has been observed 
with larger telescopes and spectroscopes, but as far 
as we know its history is closely like those of pre- 
vious Novae. At discovery its magnitude was 2 '8, or 
about the brightness of the seven stars of the Great 
Bear. The time of discovery was 2 h. 40 m. on the 
morning of February 22. Twenty-eight hours previ- 
ously Mr. Stanley Williams photographed the same 
part of the sky, and although the photograph showed 
stars fainter than the twelfth magnitude there was no 
sign of a star in the position Nova Persei afterwards 
occupied. Thus the light of the star had increased 
at least 4000 times in 28 hours. Its brightness in- 
creased for another day till it became 10 times as 
bright as at the time of discovery. It then declined 
till at the end of February it was no brighter than on 
February 22, at the end of 1901 it was of magnitude 
7*0, and at the end of 1902 of magnitude io"o. 

Before the star reached its maximum brightness its 
spectrum was examined and found to be of the Orion 
or helium type. The light from the star had passed 
through an absorbing atmosphere of hydrogen and 
helium. The next night its character had entirely 
changed and consisted of bright lines associated with 
dark lines on the side towards the violet. Some of 
the bright lines were due to hydrogen and were in 
the normal position, but the dark lines were shifted 



236 ASTRONOMY 

as much as if the absorbing atmosphere which pro- 
duced them were approaching the Earth with a 
velocity of iooo miles a second. In addition a few 
narrow lines due to sodium and calcium were dis- 
placed slightly towards the red. The same displace- 
ment was found later when the spectrum had changed, 
and showed conclusively that the star was moving 
from the Sun with a velocity of 5 miles per second. 
The large displacements of the dark lines is most 
easily explained on the assumption of a great explo- 
sion by which hydrogen was driven away from the 
star with great velocity. The spectrum of the star 
changed still further till July when the chief nebular 
line was seen, and in August and September it was 
very similar to the spectrum of a planetary nebula. 

Attempts were made to determine the parallax of the 
star without success till in the autumn of 1901 Prof. 
Max Wolf made the surprising discovery that the 
star was surrounded by a nebula. Professors Ritchey 
and Perrine of the Yerkes and Lick Observatories 
obtained photographs by giving long exposures with 
large reflecting telescopes. Two photographs taken a 
fortnight apart showed the nebula to be moving. This 
was clearly shown by comparing the position of the 
nebula with the stars near it in two photographs taken 
by Prof. Ritchey. Further photographs led to the 
conclusion that the surrounding nebula had been 
expanding continuously since the appearance of the 
star. A very interesting explanation was given by 



VARIABLE STARS AND NEW STARS 237 

Prof Kapteyn. He postulated the existence in space 
of nebulous matter, stationary and non-luminous. 
This matter became visible to us by the reflection it 




3 



Diag. XCLV. 
Nebula surrounding Nova Persei (Ritchey) 



sent of the light from the Nova. As the light travel- 
ling out from the star reached ever widening circles of 
nebulous matter it illuminated them. More than this, 
as we know 7 that light travels 186,000 miles a second, 
it was possible to infer the distance of the Nova from 
the rate at which the luminous rings spread out. This 
distance is found to be about 20 million times the 



2 3 8 ASTRONOMY 

distance of the Earth from the Sun, from which it fol- 
lows that at its greatest brilliancy Nova Persei was 
8000 times as bright as the Sun. By exposing a photo- 
graphic plate on several nights for 36 hours alto- 
gether in a little spectroscope fitted on to a large 
telescope, Prof. Perrine was able to obtain the 
spectrum of this faint nebula and found it to be 
similar to the spectrum of the star in its early stages. 
In this way it was demonstrated that the nebula shone 
by reflected light, just as the identity of the lunar 
and solar spectra could be used to prove that the 
moon's light is reflected Sun-light. 

Only a very hypothetical explanation can be given 
of the phenomena of new stars. A collision between 
two bodies is a natural supposition. But the spectro- 
scopic observations do not point to two bodies after 
the moment of collision. Apparently some conditions 
have given rise to a great outburst of hydrogen and 
helium gas from the interior of a star. The possibility 
of such an outburst is remarkable whatever the excit- 
ing cause may have been. 

The appearance of such a bright new star as Nova 
Persei is a very rare phenomenon. The photographs 
of spectra taken at Harvard College revealed five 
objects between 1893 and 1899 with the bright and 
dark line spectrum characteristic of new stars. Prob- 
ably new stars of small brilliancy are not infrequent 
occurrences. 



CHAPTER XII 

THE SIDEREAL UNIVERSE 

We have seen in previous chapters what varied 
knowledge it is possible to acquire about the stars. 
The distances of a few stars have been determined, 
and the average distances of large numbers can be 
approximately fixed. When the distances are known, 
the velocities can be determined and the luminosities 
of the stars compared with the Sun. By the study of 
double stars we are enabled in some instances to deter- 
mine the masses of stars, and from variable stars the 
sizes and densities. The spectroscope has taught us 
something of the chemistry of the stars, and of their 
temperatures and physical conditions. 

In these different w T ays the stars are shown to be 

bodies like the Sun scattered in space at distances 

apart comparable with 30 or 40 million million miles. 

The Sun is the body with which we can best compare 

them. Stars may be much bigger or smaller, denser 

or much less dense, more or less luminous. Many are 

double and some triple or quadruple. Planets may 

circulate round some of them ; on this point, however, 

we have no evidence, but only analogy for a guide. 

Sidereal astronomy, as w 7 e have seen, is divided 

239 



240 ASTRONOMY 

into two branches. One of these concerns itself 
with the physical state of the stars, and seeks to 
describe completely these states in the different stages 
of a star's history, and to follow the life of a star 
through its whole course. The other branch of 
sidereal astronomy is of a more geometrical character, 
and is concerned to describe the universe as it now 
is, to determine whether it is finite or infinite ; if finite, 
to determine its limits and the number of stars within 
them ; if infinite, to peer as far as possible into its 
infinity. These tw 7 o departments cannot be kept 
entirely separate, as it may, and does, happen that 
stars of particular kinds or in a particular stage of 
development have special geometrical relationships. 
Hydrogen stars, for example, are further from the 
Earth than those of solar type. 

When the stars are looked at as a whole, the most 
striking feature among them is the existence of the 
Milky Way, which may be seen on a clear night in 
winter reaching across the sky as a band of faint light. 
It stretches right round the celestial sphere, dividing it 
into equal parts. When examined with a telescope, 
it is found to be full of stars. The illustration (Dia- 
gram XCV) shows part of it as photographed by 
Prof. Barnard, and brings out the remarkable features 
of the dark rifts within it, or places void of stars. 
The Milky Way thus seems to be not one but a 
number of agglomerations of stars. It certainly con- 
tains a vast number of faint stars. Does it also con- 



THE SIDEREAL UNIVERSE 



24 1 



tain bright ones, or are the bright ones apparently in 
it much nearer to the Sun and merely seen projected 
against it ? An answer can be given to this question 
by counting the number of bright stars in the dark 




Diag. XCV. 
Part of Milky Way {Barnard). 



rifts and comparing the result with the number in an 
equal area where the faint stars are thick. In this way 
it is found that a considerable number of bright stars 
really belong to the galaxy. 



242 ASTRONOMY 

The physical characteristics of the stars show some 
relationship to the Milky Way. Speaking generally, 
the stars in it are blue, and the remarkable Wolf- 
Rayet stars are wholly confined to it. New stars, too, 
usually appear in the Milky Way. 

When the number of stars of given magnitudes in 
different parts of the sky is counted, it is found that 
the density or number per square degree increases 
with fair uniformity from the poles of the Milky Way 
to the Milky Way itself. But this increase in density 
is much more pronounced for the faint than for the 
bright stars. If we take stars brighter than 5*5 mag. 
there are on the average 4*63 in every 100 square 
degrees near the pole of the Milky Way and 9*07 in 
the Milky Way itself, or a proportion of 1 : 1*96. For 
stars of magnitude 8*5 to 9*5 the numbers are 235 and 
595, and the proportion 1 : 2*53. For stars of magni- 
tude ii'5 to 12*5 the numbers are 3330 and 15,400, 
and the proportion 1 : 4*62. The proportion increases 
very rapidly for higher magnitudes. Moreover, the 
numbers increase gradually as the Milky Way is 
approached and do not suddenly alter, as if the Milky 
Way were entirely distinct from the other stars. 

When we consider proper motions, and these are 
a fair index of the average distances of the stars, it 
is found that stars of large proper motion are dis- 
tributed pretty equally in all directions. Prof. New- 
comb points out that the number of stars whose 
proper motion is greater than 5 /; a century is no 



THE SIDEREAL UNIVERSE 243 

greater in the Milky Way than at a distance from it. 
Now in a century the Sun moves a distance equal to 
400 times its distance from the Earth, and will there- 
fore produce a movement of 5 ;/ in a star whose parallax 
* s tw " or o'oi25", which corresponds to a distance of 
16 million times the Sun's distance. The Milky Way 
therefore lies beyond this limit. This is to be 
taken as an example of the method of reasoning, as 
the numerical result is very far less than the probable 
distance of the Milky Way. 

As the Milky Way divides the sky into equal parts, 
the Sun is situated in its plane. We do not know 
how far it may be from the centre, for as yet the dis- 
tance to the Galaxy in different directions has not been 
determined. It would seem that the universe of stars 
extends much further in the direction of the Milky 
Way than in that perpendicular to it. Its boundary 
is irregular, but nowhere nearer than 200 million 
times the Sun's distance. Whether the agglomera- 
tions which form the Milky Way are near this bound- 
ary, or whether we see some stars w-hich are quite 
beyond them is as yet unknown. As far as we can 
tell, the number of stars, though very great, is finite. 
But there are some indications that light is absorbed 
in its passage through space, and our conclusions 
must be very guarded. We are obliged to say with 
Laplace, "Ce que nous connaissons est peu de chose, 
ce que nous ignorons est immense." 



INDEX 



Aberration of light, 94-96 
Achromatic object glass, 70 
Algol, 225-228 
Almagest, Ptolemy's, 28-29 
Apse, 22 

Calendar, 5 

Cavendish experiment, 61-62 

Chemistry of stars, 193-200 ; of 

sun, 1 09- 1 12 
Chromosphere, sun's. 11 6-1 19 
Circles, divided, 65-67, JJ 
Clocks, 65 

Clusters of stars, 220-224 
Copernican system, 30-37 
Comets, 51, 149-157, 160- 1 61 
Corona, sun's, 119-121, 128 

Declination, 63-64 
Density, of earth, 61-62 ; of 
sun, 101 ; of planet?, 133 ; of 
Algol, 228 ; of £ Lyrae, 230 
Distance of moon, 26-28 
„ of planets, 43 
„ of stars, 170-179, 187- 

190 
,, of sun, 28, 85-99 
Diurnal movement of stars, 

9-13, 3o 
„ movement of sun, 2-4 

„ rotation of earth, 30- 

3i 
Doppler^s Principle, 124 
Double stars, 208-215 \ spectro- 
scopic, 215-220 



Dusky layer round the sun, 
113-114 

Earth, density, 61-62 ; shape, 

49 ; size, 26 
Eccentricity of earth's orbit, 22 
Eclipse of moon, 18-19, 26-27 ; 

of sun, 17-18 
Eclipsing stars, 225-228 
Ecliptic, 1 5 
Ellipse, 42, 52 
Elliptic motion, 42, 46-47 
Epicyclic movement, 21, 33 
Equatorial mounting, 78-79 
Equinoctial, 16 
Eros, 91-93 

Fixed stars, 9-13, 1 64- 1 6 5 

Galileo, 37-40, 45 

G?'a?iulation of sun's surface, 

114-115 
Gravitation, 45-62, 98-99 

H alley's comet, 56-58 
Heliometer, 81-82 
Hipparchus, 21-25, 26-27 
Hyperbola, 52 

Jupiter, 38, 130, 132, 133, 135, 
136, 144-146 

Kepler's Laws, 42-44 



Lens, 67 

Light, aberration of, 94-96 



245 



246 



INDEX 



Light, velocity of, 93-94, 96-97 
Luminosities of stars, 191-192 

Magnitude, stellar, 166-168 
Mars, 130, 133, 134-135 

,, opposition of, 86-88, 89-91 
Mass, determination of, 52-53 

„ of earth, 60-62 

„ of planets, 132-133 

„ of stars, 213-215, 228, 
230 

„ of sun, 101 
Mercury, 34-35, 130, 131, 133, 

134, 140 
Meridian, 64 
Meteors, 1 57-161 
Melon's cycle, 8 
Micrometer, yy, So 
Milky Way, 240-243 
Minor planets, 1 30- 1 3 1 
Month, 7-8 
M0071, distance of, 26-28 

,, eclipses of, 18-19, 26-27 

„ features of, 37-38, 146-148 

„ history of, 163 

„ movement of, 7, 22-23, 
58-60 

„ phases of, 6 
Motion in line of sight, 185-187 
Movement of planets among the 

stars, 19-21, 33-35 

Nebula?, 201-207 

Nebular hypothesis, 1 6 1 - 1 63 

Neptune, 56, 130, 132, 133, 134, 

139, 141, 142 
New stars, 234-238 
Newton, 46-54, 69, 71 
Number of stars, 1 68 -1 70 

Parabola, 52 
Parallax, solar, 86-93 

„ stellar, 170-179 
Phases of the moon, 6-7 



Precession of the equinoxes, 23- 

25,50-51 
Principia, Newton's, 54 
Prominences, solar, 116-119 
Proper motions, stellar, 179-185 
Ptolemy's Almagest, 28-29 

Radiation, solar, 102-103 
Reflecting telescope, 71-73 
Refracting telescope, 67-7 1 
Revolution of earth round sun, 

31-33 
Right ascension, 63 
Rotation of earth on its axis, 

3°-3i, 39 
„ of planets, 133, 134 
„ of sun, 39, 123-126 

Saros, 19 

Satellites, 134-136 

Saturn, 130, 132, 133, 136-138, 

141 
Schehallien, attraction of, 60-61 
Shape of earth, 25, 49 
Size of earth, 25-26 
„ of planets, 131-132 
„ of sun, 100-101 
Solar che?nistry, 109-1 12 
, , prominences, 1 1 6- 1 1 9 
„ radiation, 102-103 
„ spectrum, 110-112 
Spectra, different kinds of, 108, 
109 
„ of comets, 153, 157; of 
nebulas, 201-202,204; 
of planets, 141, 142 ; 
of stars, 194-200 ; of 
sun, 110-112 
Speciroheliograph, 1 2 1 - 1 2 2 
Spectroscope, 106-109 
Spectroscopic binaries, 215-220 
Stars, names of, 165-166 ; cata- 
logues of, 166 ; light of, 170, 
191-192 ; magnitudes, 166- 



INDEX 



247 



168 ; distance of, 170-179, 
187-190 ; velocities of, 190- 

191 ; absolute luminosity, 191 — 

192 ; spectra of, 193-200 
Sun, 100-128 

Sun's corona, 119, 1 2 1 - 1 2 8 
,, distance, 85-99 
„ heat, maintenance of, 103- 

105 
„ motion in space, 182-185 
„ temperature, 105-106 
„ spots, 39, 112, 1 1 5- 1 16, 
126-128 
Stability of solar system, 55 

Telescope, 37, 67-84 
Temperature of pla7iets, 1 39- 1 4 1 

„ of sim, 105-106 

Tides, 49-50 



Transit circle, 74-78 

Types of stellar spectra, 195-200 

Uranus, 130, 132, 133, 138, 139, 
141, 142 

Variable stars of lo?ig period, 

232-234 
Variable stars of short period, 

225-232 
Velocities of stars, 190-191 
Velocity of solar system, 1 8 J 
Venus, 34-35, 38, 130, 131, 133, 
134, 139, 140, 141 
„ transit of, 88-89 

Zenith, 64 
Zodiac, 7-16 



THE END 



Richard Clay & Sons, Limited, 

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